Mark throws a ball to Daniel with an initial speed of 20 m/s at an angle of 45 degrees.If they are initially 55 m apart,calculate the average speed Daniel has to run to catch the ball.(Assume the ball is thrown and caught at the same height.Also assume that Daniel starts to run when the ball is thrown.)
A)19 m/s
B)14 m/s
C)4.9 m/s
D)9.1 m/s
E)2.9 m/s

Question

Quizplus · Accepted Answer

We can use the kinematic equation to find the time it takes for the ball to reach Daniel:
Δy = viy*t + 1/2*a*t^2
Since the ball is thrown and caught at the same height, Δy = 0.
viy = 20*sin(45) = 14.1 m/s (the initial vertical componentof the velocity)
a = -9.8 m/s^2 (the acceleration due to gravity)
So, 0 = 14.1*t + 1/2*(-9.8)*t^2
Solving for t, we get t ≈ 2.86 s
In this time, the ball travels a horizontal distance of:
Δx = vix*t = 20*cos(45)*2.86 ≈ 40.3 m
So, Daniel has to run 55 - 40.3 = 14.7 m to catch the ball.
The average speed is distance traveled divided by time taken:
average speed = 14.7/2.86 ≈ 5.14 m/s
Therefore, the closest answer choice is C) 4.9 m/s.

Mark Throws a Ball to Daniel with an Initial Speed