5. Projectile Motion

You throw a rock off the top of a tall building at an upward angle of 15°. At t=3 s, the rock's horizontal displacement from you is 52m. How high does the rock get above the top of the building?

A ball is thrown from the top of a 50-m-tall building with a speed of 40 m/s at an angle of 37° above the horizontal. How far horizontally does the ball travel before hitting the ground?

(II) You buy a plastic dart gun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 3.4 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?

Apollo astronauts took a 'nine iron' to the Moon and hit a golf ball about 180 m. Assuming that the swing, launch angle, and so on, were the same as on Earth where the same astronaut could hit it only 32 m, estimate the acceleration due to gravity on the surface of the Moon. (We neglect air resistance in both cases, but on the Moon there is none.)

A child runs down a 12° hill and then suddenly jumps upward at a 15° angle above horizontal and lands 1.3 m down the hill as measured along the hill. What was the child's initial speed at the jump?

(II) An Olympic long jumper is capable of jumping 8.0 m. Assuming his horizontal speed is 9.1 m/s as he leaves the ground, how long is he in the air and how high does he go? Assume that he lands standing upright—that is, the same way he left the ground.

A grasshopper hops along a level road. On each hop, the grasshopper launches itself at angle θ₀ = 45 ° and achieves a range R = 0.80 m . What is the average horizontal speed of the grasshopper as it hops along the road? Assume that the time spent on the ground between hops is negligible. 

(II) A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 62.0 m/s at an angle of 35.0° with the horizontal, as shown in Fig. 3–45.

(a) Determine the time taken by the projectile to hit point P at ground level.

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(II) A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 62.0 m/s at an angle of 35.0° with the horizontal, as shown in Fig. 3–45.

(b) Determine the distance X of point P from the base of the vertical cliff. At the instant just before the projectile hits point P.                                                                       

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(II) A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 62.0 m/s at an angle of 35.0° with the horizontal, as shown in Fig. 3–45. At the instant just before the projectile hits point P, find

(c) the horizontal and the vertical components of its velocity

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(II) If a ball is kicked from ground level at 15.0 m/s, there are two launch angles that will make the ball land 20.0 m away.

(b) What maximum height does the ball reach in each case?

(II) An athlete performing a long jump leaves the ground at a 27.0° angle and lands 7.80 m away.

(a) What was the takeoff speed?

(II) A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 62.0 m/s at an angle of 35.0° with the horizontal, as shown in Fig. 3–45.. At the instant just before the projectile hits point P, find

(d) the magnitude of the velocity,

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(II) A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 62.0 m/s at an angle of 35.0° with the horizontal, as shown in Fig. 3–45. At the instant just before the projectile hits point P, find

(e) the angle made by the velocity vector with the horizontal.

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(II) A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 62.0 m/s at an angle of 35.0° with the horizontal, as shown in Fig. 3–45. At the instant just before the projectile hits point P,

(f) Find the maximum height above the cliff top reached by the projectile.

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At t = 0 a batter hits a baseball with an initial speed of 28 m/s at a 55° angle to the horizontal. An outfielder is 85 m from the batter at t = 0 and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of 22° with the plane in which the ball moves (see Fig. 3–66). What speed and direction must the fielder take to catch the ball at the same height from which it was struck? Give the angle with respect to the outfielder's line of sight to home plate.

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A diver leaves the end of a 3.5-m-high diving board and strikes the water 1.3 s later, 3.0 m beyond the end of the board. Considering the diver as a particle, determine:

(a) her initial velocity, v₀ (→ above v);

(II) Romeo is throwing pebbles gently up to Juliet's window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 8.0 m below her window and 8.5 m from the base of the wall (Fig. 3–48). How fast are the pebbles going when they hit her window?

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