A spring-loaded toy gun shoots a $3.0\mathrm{g}$ plastic ball straight up into the air. From the position of the ball when the gun is cocked, with the spring compressed, to the maximum height the ball reaches, is $2.5\mathrm{m}$. If the spring was compressed $2.0\mathrm{cm}$, what is the spring constant of the spring? Ignore air resistance.

(III) Early test flights for the space shuttle used a “glider” (mass of 980 kg including pilot). After a horizontal launch at 480 km/h at a height of 3200 m, the glider eventually landed at sea level with a speed of 210 km/h.

(a) What would its landing speed have been in the absence of air resistance?

You are practicing jumping as far as you can. In one attempt, you run and leave the floor with 7 m/s directed at an unknown angle. What maximum height do you reach if your speed at that point is 5 m/s? Ignore air resistance.

A film of Jesse Owens’s famous long jump (Fig. 8–48) in the 1936 Olympics shows that his center of mass rose 1.1 m from launch point to the top of the arc. What minimum speed did he need at launch if he was traveling at 6.5 m/s at the top of the arc?

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(III) Early test flights for the space shuttle used a “glider” (mass of 980 kg including pilot). After a horizontal launch at 480 km/h at a height of 3200 m, the glider eventually landed at sea level with a speed of 210 km/h.

(a) What would its landing speed have been in the absence of air resistance?