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 gray kangaroo can bound across level ground with each jump carrying it 10 m from the takeoff point. Typically the kangaroo leaves the ground at a 20° angle. If this is so: What is its maximum height above the ground?

In the absence of air resistance, a projectile that lands at the elevation from which it was launched achieves maximum range when launched at a 45° angle. Suppose a projectile of mass m is launched with speed into a headwind that exerts a constant, horizontal retarding force ${\vec{F}}_{\text{wind}}=-F_{\text{wind}}\hat{ı}.$. Find an expression for the angle at which the range is maximum.

In the absence of air resistance, a projectile that lands at the elevation from which it was launched achieves maximum range when launched at a 45° angle. Suppose a projectile of mass m is launched with speed into a headwind that exerts a constant, horizontal retarding force ${\vec{F}}_{\text{wind}}=-F_{\text{wind}}\hat{ı}.$ By what percentage is the maximum range of a 0.50 kg ball reduced if $F_{\text{wind}}=0.60\text{ N}$?

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?

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. 

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

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

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 the horizontal and the vertical components of its velocity.