A soccer player claims that he can kick the ball over a wall of height $3.5 \mathrm{m}$ which is $32 \mathrm{m}$ away along a horizontal field. The player punts the ball from an elevation of $1.0 \mathrm{m}$ and the ball is projected at an initial speed of $18 \mathrm{m} {\mathrm{s}}^{-1}$ in the direction $40°$ from the horizontal. Does the ball clear the wall?

 You throw a ball toward a wall at speed $25.0 \mathrm{m} {\mathrm{s}}^{-1}$ and at angle ${\text{θ}}_0=$ $40.0°$ above the horizontal in figure shown below The wall is distance $d=22.0 \mathrm{m}$ from the release point of the ball.
(a) How far above the release point does the ball hit the wall? What are the (b) horizontal and (c) vertical components of its velocity as it hits the wall? (d) When it hits, has it passed the highest point on its trajectory?

A defense air force plane, diving with constant speed at an angle of $52.0^{°}$ with the vertical, drops a shell at an altitude of $720 \mathrm{m}$. The shell reaches the ground $6.00 \mathrm{s}$ after its release.

(a) What is the speed of the plane?

(b) How far does the shell travel horizontally during its flights? What are the 

(c) horizontal and

(d) vertical components of its velocity just before reaching the ground? Assume an $x$-axis in the direction of the horizontal motion and an upward $y$-axis.

A trebuchet was a hurling machine built to attack the walls of a castle under siege. A large stone could be hurled against a wall to break apart the wall. The machine was not placed near the wall because the arrows could reach it from the castle wall. Instead, it was positioned, so that, the stone hit the wall during the second half of its flight. Suppose a stone is launched with a speed of $v_{\mathrm{B}}=30.0 \mathrm{m} {\mathrm{s}}^{-1}$ and at an angle of ${\text{θ}}_0=40.0^{°}$. What is the speed of the stone if it hits the wall

(a) Just as it reaches the top of its parabolic path and

(b) when it has descended to half that height?

(c) As a percentage, how much faster is it moving in part (b) than in part (a)?

A rifle that shoots bullets at $460 \mathrm{m} {\mathrm{s}}^{-1}$ is to be aimed at a target $45.7 \mathrm{m}$ away. If the center of the target is level with the rifle, how high above the target must the rifle barrel be pointed so that the bullet hits dead center?

During a tennis match, a player serves the ball at $23.6 \mathrm{m} {\mathrm{s}}^{-1}$, with the center of the ball leaving the racquet horizontally $2.42 \mathrm{m}$ above the court surface. The net is $12 \mathrm{m}$ away and $0.90 \mathrm{m}$ high. When the ball reaches the net,

(a) does the ball clear it and

(b) what is the distance between the center of the ball and the top of the net?

Suppose that, instead, the ball is served as before but now it leaves the racquet at $5.{00}^{°}$below the horizontal when the ball reaches the net,

(c) does the ball clear it and

(d) what now is the distance between the center of the ball and the top of the net?

From the platform edge located at $12.0 \mathrm{m}$ above the surface of the water, a high champion pushes off horizontally with a speed of $2.50 \mathrm{m} {\mathrm{s}}^{-1}$.

(a) At what horizontal distance from the edge is the diver $0.900 \mathrm{s}$ after pushing?

(b) At what vertical distance above the surface of the water is the diver just then?

(c) At what horizontal distance from the edge does the diver strike the water?

A golf ball is struck at ground level. The speed of the golf ball as a function of the time is shown in the figure, where, $t=0$ at the instant the ball is struck. The scaling on the vertical axis is set by $v_{\mathrm{a}}=19 \mathrm{m} {\mathrm{s}}^{-1}$ and $v_{\mathrm{b}}=31 \mathrm{m} {\mathrm{s}}^{-1}$.

(a) How far does the golf ball travel horizontally before returning to ground level?

(b) What is the maximum height above ground level attained by the ball?

In the figure below, a ball is thrown leftward from the left edge of the roof, at height $h$ above the ground. The ball hits the ground $1.50 \mathrm{s}$ later, at distance $d=25.0 \mathrm{m}$ from the building and at angle $\mathrm{\theta }=60.0^{°}$ with the horizontal.

(a) Find $h$ (Hint: One way is to reverse the motion, as if on video.)

(b) What is the magnitude?

(c) What is the angle relative to the horizontal of the velocity at which the ball is thrown?

(d) Is the angle above or below the horizontal?