4. 2D Kinematics

Acceleration in 2D

Multiple Choice
A football at rest is kicked by a football kicker. The ball is in contact with the kicker's foot for 0.050s, during which it experiences an acceleration a = 340 m/s². The ball is launched at an angle of 40° above the ground (x-axis). Calculate the horizontal and vertical components of the launch velocity.
Multiple Choice
A particle's velocity is given by $\overset{⇀}{v} = (3 t \frac{m}{s}) \hat{i} + (4 t^{3} \frac{m}{s}) \hat{j}$ . What are the x and y components of its acceleration at $t = 2 s$ ?
Open Question
(II) A car is moving with speed 16.0 m/s due south at one moment and 25.7 m/s due east 8.00 s later. Over this time interval, determine the magnitude and direction of (a) its average velocity, (b) its average acceleration. (c) What is its average speed? [Hint: Can you determine all these from the information given?]
Open Question
A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by v = [5.00 m/s − (0.0180 m/s3)t2]î + [2.00 m/s + (0.550 m/s2)t]ĵ. (b) What are the magnitude and direction of the car's velocity at t = 8.00 s? (b) What are the magnitude and direction of the car's acceleration at t = 8.00 s?
Open Question
The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt2, where α = 2.4 m/s and β = 1.2 m/s2. (c) Calculate the magnitude and direction of the bird's velocity and acceleration at t = 2.0 s.
Open Question
(a) Complete the motion diagram by adding acceleration vectors.
Open Question
A rocket-powered hockey puck moves on a horizontal frictionless table. Figure EX4.7 shows graphs of and , the x- and y-components of the puck's velocity. The puck starts at the origin. What is the magnitude of the puck's acceleration at t = 5s?
Open Question
(II) On mountainous downhill roads, an escape lane is sometimes placed to the side of the road for trucks whose brakes might fail. Assuming a constant upward slope of 26°, calculate the horizontal and vertical components of the acceleration of a truck that slowed from 110 km/h to rest in 7.0 s. See Fig. 3–43.
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Open Question
(I) A diver running 2.5 m/s dives out horizontally from the edge of a vertical cliff and 3.5 s later reaches the water below. How high was the cliff and how far from its base did the diver hit the water?
Open Question
(II) A ball thrown horizontally at 10.8 m/s from the roof of a building lands 21.0 m from the base of the building. How high is the building?