Answer to Question #262837 in Physics for Mix

Question #262837

Ellen throws a ball toward a wall at speed 30.0 m/s and at angle 45.0° above the

horizontal. The wall is distance 25.0 m from the release point of the ball.

a) (5%) How far above the release point does the ball hit the wall?

b) (5%) What is the horizontal component of its velocity as it hits the wall?

c)

(5%) What is the vertical component of its velocity as it hits the wall?

d

(5%) When it hits, has it passed the highest point on its trajectory?


1
Expert's answer
2021-11-08T09:11:42-0500

(a) Let's first find the time that the ball takes to hit the wall:


x=v0xt=v0tcosθ,x=v_{0x}t=v_0tcos\theta,t=xv0cosθ=25.0 m30.0 ms×cos45.0=1.18 s.t=\dfrac{x}{v_0cos\theta}=\dfrac{25.0\ m}{30.0\ \dfrac{m}{s}\times cos45.0^{\circ}}=1.18\ s.

Then, we can find how far above the release point the ball hits the wall from the kinematic equation:


y=v0yt12gt2,y=v_{0y}t-\dfrac{1}{2}gt^2,y=v0tsinθ12gt2,y=v_0tsin\theta-\dfrac{1}{2}gt^2,y=30.0 ms×1.18 s×sin45.012×9.8 ms2×(1.18 s)2=18.21 m.y=30.0\ \dfrac{m}{s}\times1.18\ s\times sin45.0^{\circ}-\dfrac{1}{2}\times9.8\ \dfrac{m}{s^2}\times(1.18\ s)^2=18.21\ m.

(b) We can find the horizontal component of ball's velocity as it hits the wall as follows:


vx=v0cosθ=30.0 ms×cos45.0=21.21 ms.v_x=v_0cos\theta=30.0\ \dfrac{m}{s}\times cos45.0^{\circ}=21.21\ \dfrac{m}{s}.

(c) We can find the vertical component of ball's velocity as it hits the wall as follows:


vy=v0sinθgt,v_y=v_0sin\theta-gt,vy=30.0 ms×sin45.09.8 ms2×1.18 s,v_y=30.0\ \dfrac{m}{s}\times sin45.0^{\circ}-9.8\ \dfrac{m}{s^2}\times1.18\ s,vy=9.65 ms.v_y=9.65\ \dfrac{m}{s}.

(d) As we can see from the calculations, when the ball hits the wall vy>0v_y>0. It means that the ball has not reached the highest point on its trajectory.


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