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 $F_{\text{wind}}=0.60\text{ N}$?

In Problems 78, 79, and 80 you are given the equations that are used to solve a problem. For each of these, you are to write a realistic problem for which these are the correct equations. Be sure that the answer your problem requests is consistent with the equations given.

$\begin{aligned}100 \, \text{m} &= 0 \, \text{m} + (50 \cos \theta \, \text{m/s}) t_1 \\0 \, \text{m} &= 0 \, \text{m} + (50 \sin \theta \, \text{m/s}) t_1 - \frac{1}{2} (9.80 \, \text{m/s}^2) t_1^2\end{aligned}$

A physics student on Planet Exidor throws a ball, and it follows the parabolic trajectory shown in FIGURE EX4.13. The ball's position is shown at 1 s intervals until t = 3s. At t = 1s, the ball's velocity is v = (2.0 i + 2.0 j) m/s. Determine the ball's velocity at t = 0 s, 2s, and 3s.

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.

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?

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. 

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.