A Frisbee gets stuck in the top of a tree, 60 meters above the ground. What is the smallest initial velocity you could throw a ball to reach the Frisbee and dislodge it?
A. 48.5 m/s from an angle of 45 degrees above the horizontal
B.48.5 m/s from directly underneath the ball
C.34.4 m/s from directly underneath the ball
D.34.4 m/s from an angle of 45 degrees above the horizontal
if the ball was dropped from 60 m, what would be its impact velocity?
m g h = 1/2 m v^2 ... v = √(2 g h)
Pls give me the answer
To determine the smallest initial velocity required to reach the Frisbee, we can analyze the motion of the ball using the principles of projectile motion.
In projectile motion, the vertical and horizontal components of motion can be considered separately. In this case, we need to focus on the vertical component to reach the Frisbee at the top of the tree.
The vertical motion of the ball can be described by the equation:
y = y0 + v0y * t - 1/2 * g * t^2
Where:
y is the vertical displacement (60 meters in this case)
y0 is the initial vertical position (0 meters, as we start from the ground)
v0y is the vertical component of initial velocity
g is the acceleration due to gravity (-9.8 m/s^2)
t is the time taken to reach the top of the tree
To find the smallest initial velocity, we need to determine the time taken (t) to reach the top of the tree.
At the topmost point of the trajectory, the vertical velocity component (v0y) becomes zero. So, we can use the following equation to find the time taken to reach the top:
v0y = g * t
Rearranging the equation, we can solve for t:
t = v0y / g
Now, let's evaluate each option and find the time taken in each case:
A. 48.5 m/s from an angle of 45 degrees above the horizontal:
The vertical component of velocity is given by v0y = v0 * sin(theta). So, v0y = 48.5 m/s * sin(45 degrees) = 48.5 m/s * 0.707 ≈ 34.4 m/s
Using this value in the equation t = v0y / g, we get:
t = 34.4 m/s / 9.8 m/s^2 ≈ 3.51 seconds
B. 48.5 m/s from directly underneath the ball:
In this case, the initial vertical velocity component (v0y) is zero. Therefore, the ball will not reach the Frisbee.
C. 34.4 m/s from directly underneath the ball:
In this case, the initial vertical velocity component (v0y) is zero. Therefore, the ball will not reach the Frisbee.
D. 34.4 m/s from an angle of 45 degrees above the horizontal:
Using the same formula as before, we find v0y = 34.4 m/s * sin(45 degrees) = 34.4 m/s * 0.707 ≈ 24.37 m/s
Using this value in the equation t = v0y / g, we get:
t = 24.37 m/s / 9.8 m/s^2 ≈ 2.49 seconds
From our calculations, the smallest initial velocity that will allow the ball to reach the Frisbee and dislodge it is option D: 34.4 m/s from an angle of 45 degrees above the horizontal.