5. Projectile Motion

The cannon in FIGURE CP4.83 fires a projectile at launch angle θ with respect to the slope, which is at angle Φ. Find the launch angle that maximizes d. Hint: Choosing the proper coordinate system is essential. There are two options.

Jim pushes a penny off a $0.86\mathrm{m}$ tall table. Assume the penny is moving horizontally as it leaves the table at 5 m/s. How long is the penny in the air? Ignore air resistance.

Bob throws a ball from his second story window to his friend Steve who is on the ground below. Assume that Bob throws the ball horizontally at $10\mathrm{m}/\mathrm{s}$, and Steve will catch the ball at a point $4.5\mathrm{m}$ below Bob. How far from the base of the building should Steve stand in order to catch the ball?

A daring 510-N swimmer dives off a cliff with a running horizontal leap, as shown in Fig. E3.10. What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom, which is 1.75 m wide and 9.00 m below the top of the cliff?

Crickets Chirpy and Milada jump from the top of a vertical cliff. Chirpy drops downward and reaches the ground in 2.70 s, while Milada jumps horizontally with an initial speed of 95.0 cm/s. How far from the base of the cliff will Milada hit the ground? Ignore air resistance.

A physics book slides off a horizontal tabletop with a speed of 1.10 m/s. It strikes the floor in 0.480 s. Ignore air resistance. Find (a) the height of the tabletop above the floor;

A rifle is aimed horizontally at a target 50 m away. The bullet hits the target 2.0 cm below the aim point. (b) What was the bullet's speed as it left the barrel?

You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. You find the arrow stuck in the ground 60 m away, making a 30° angle with the ground. How fast was the arrow shot?

On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hit the ball with a speed of 25 m/s at an angle 30 degrees above the horizontal. (b) For how much more time was the ball in flight?

A cannonball is fired at 100 m/s from a barrel tilted upward at 25°.c. What is the angle after the cannonball travels 500 m?

A projectile's horizontal range over level ground is v₀² sin 2θ/g. At what launch angle or angles will the projectile land at half of its maximum possible range?

A projectile is launched from ground level at angle θ and speed v₀ into a headwind that causes a constant horizontal acceleration of magnitude a opposite the direction of motion.a. Find an expression in terms of a and g for the launch angle that gives maximum range.

A projectile is launched from ground level at angle θ and speed v₀ into a headwind that causes a constant horizontal acceleration of magnitude a opposite the direction of motion.b. What is the angle for maximum range if a is 10% of g?