Two children are playing on two trampolines. The first child b...

Question

Two children are playing on two trampolines. The first child bounces up one-and-a-half times higher than the second child. The initial speed upwards of the second child is 4.0 m/s.

(b) What is the initial speed of the first child?

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. At the exact same moment, two balls are thrown vertically upwards into the air. The second ball reaches a height that is 2.50 times higher than the first ball. Calculate what the initial speed of the second ball will be given that the initial speed of the first ball is 5.00 m per second. So that's our goal. We're trying to figure out the initial speed the velocity of the second ball. Like what is that value gonna be given that the initial speed or the velocity of the first ball is 5.00 m per second? Awesome. We're also given some multiple choice answers. They're all in the same units of meters per second. So let's read them off to see what our final answer might be. A is 7.91 B is 5.59 C is 6.25 and D is 12.5. Awesome. So first off, let us consider the upwards motion to be positive and that the initial distance why to the subscript of I so Y I, which is the initial distance sequel to 0 m to be the ground level. So this is the ground level and I'm just gonna say ground. So we don't get confused. OK? From where the balls are thrown up from. So now we must recall and use the uniformly accelerated motion equations. U AM for short to calculate the height that is reached by the first ball. And let's call this equation one. So to calculate the height that is reached by the first ball, we know that the final velocity of the first ball. So VF one squared is equal to the velocity. You know the initial velocity I should say of the first ball squared plus two multiplied by the acceleration of ball one or the first ball multiplied by the change and Y delta Y of one. So VF one is equal to 0 m per second. So the final velocity at the maximum height is zero and V I one which I is equal to 5.00 m per second is the initial velocity. And a one is the acceleration due to gravity. In this case, it's negative because it's gravity is fighting the ball since the balls are thrown upward into the air and gravity is trying to bring those balls back to the ground. And delta Y one here. This is important, you need to make a note. So delta Y one is equal to Y one minus zero in units of meters. So it's equal to Y 1 m. So this is the final height reached in units of meters. So now we can plug in all of our known variables into equation one and solve. And in this case, we're given everything but the value for Y one as you noticed. So the final velocity for this case is 0 m per second squared is equal to 5.00 m per second squared plus two multiplied by negative. So this is gravity. The acceleration is gravity. So negative 9.81 m per second squared, as you should recall for the value for gravity and as we discovered delta Y one is equal to Y one. And just for simplicity's sake, don't forget the meter since we're trying to find our Y one value in meters. So the seconds will cancel out leaving us with just meters which is good and we'll see that more in a second. So simplifying rearranging to sulfur Y one, we'll get that. Y one is equal to 5.00 m per second square divided by two, multiplied by 9.81 m per second squared. So when we plug into a calculator, we will get 1.2742099 but we can round to just three decimal places. To keep things short and simple. So I'll get 1.274 m when we round to three decimal places. But at this point, we need to note that the second ball reaches a height of 2.50 times that of the first ball. So we need to state that Y two, since this is the, the height for the second ball is equal to 2.50 multiplied by Y one. So 2.50 multiplied by Y one value which we just found to be 1.274 meters is equal to 3.185 m. Awesome. So now we need to solve for the initial speed of the second ball using equation one but focusing on ball number two instead. So let's do that. So the final velocity for ball two is equal to the initial velocity of ball two squared. So the final velocity squared is equal to the initial velocity squared and this is focusing on ball number two, everybody. OK. So plus two multiplied by the acceleration for the second ball multiplied by the change in why? For two? Since we're focusing on ball two, say that a bunch of times, we need to avoid confusion here. OK. So doing a quick little run through. So the final velocity of ball two is 0 m per second at the maximum height. So when you toss this ball straight up into the air for a brief second once it reaches its maximum height right before it starts to fall back to the ground. So for a split second, it's at 0 m per second and then it will start falling back down to earth. We do not know what the initial velocity of ball two is. That's an unknown value to us. And the acceleration for the second ball is due to gravity. It's also in the negative direction because it's falling like the first ball was. So it's negative 9.81 m per second squared. And then let's make a little note here. So for delta Y two, like above, we need to know the height for ball two minus 0 m is equal to 3.185 m for the final height reached by ball number two. So that's the value we just found for Y two. Awesome. So at this point, we can now plug in all of our known variables. And as I mentioned, we do not know the initial velocity. So we're gonna plug in all of our known variables and then we're gonna have to rearrange everything to solve for the initial velocity. So let's do that. So the final velocity is 0 m per second squared, which is equal to the initial velocity of ball two squared plus two, multiplied by negative 9.81 m per second squared multiplied by our Y two value which was 3.185 m as we just found a few seconds ago or I should say a few minutes ago. So now this is where the algebra and the rearranging comes in. So we can square balls like we could shuffle things around square both sides. So we'll get that. The initial velocity of ball two squared is equal to 62.4897 meters squared divided by second squared or meter squared per second squared. And then this is where you square both sides to get rid of the squared on the initial velocity. So the initial velocity for ball two is equal to and this is you have to take the square root of both sides now and you'll get 7.905 0 m per second, which we can round to a simple 7.91 when we round to two decimal places because this five will round the 0 to 1. Awesome. So our final answer for the initial velocity for ball two has to be 7.91 m per second. Fantastic. So looking at our multiple choice answers, the correct answer as to be the letter A which is 7.91 m per second. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Struggling with Physics?

Two children are playing on two trampolines. The first child bounces up one-and-a-half times higher than the second child. The initial speed upwards of the second child is 4.0 m/s.

(b) What is the initial speed of the first child?

Watch next

Vertical Motion and Free Fall practice set

Struggling with Physics?

Two children are playing on two trampolines. The first child bounces up one-and-a-half times higher than the second child. The initial speed upwards of the second child is 4.0 m/s.(b) What is the initial speed of the first child?

Watch next

Vertical Motion and Free Fall practice set

Two children are playing on two trampolines. The first child bounces up one-and-a-half times higher than the second child. The initial speed upwards of the second child is 4.0 m/s.

(b) What is the initial speed of the first child?