A 0.30 ball is thrown with a speed of 13 at an angle of 32.
What is its speed at its highest point?
To find the speed of the ball at its highest point, we need to analyze the motion of the ball and understand the concept of projectile motion.
1. First, we divide the motion into vertical and horizontal components. The vertical component is affected by the force of gravity, and the horizontal component remains constant because no force acts on it.
2. Since the ball is at its highest point, the vertical component of its velocity is zero because the ball momentarily stops moving upwards before falling back down.
3. To calculate the vertical component of the initial velocity, we use the equation v_fy = v_iy + gt, where v_fy is the final vertical velocity (zero at the highest point), v_iy is the initial vertical velocity, g is the acceleration due to gravity (-9.8 m/s^2), and t is the time taken to reach the highest point.
4. By rearranging the equation, we get v_iy = -gt. Since g is negative (acting downwards), we substitute g = -9.8 m/s^2 and solve for v_iy.
v_iy = - (-9.8 m/s^2) × t
5. To find the time taken to reach the highest point, we need to consider the vertical component of the initial velocity and the acceleration due to gravity. As we know, the initial velocity is v_i = 13 m/s at an angle of 32 degrees, and we can find v_iy using the equation v_iy = v_i × sin(theta), where theta is the angle of projection.
v_iy = 13 m/s × sin(32 degrees)
6. Now, substitute the value of v_iy in the equation from Step 4 and solve for t.
v_iy = - (-9.8 m/s^2) × t
13 m/s × sin(32 degrees) = 9.8 m/s^2 × t
7. Calculate t using the equation above.
8. Once we have the time taken to reach the highest point, we can use it to find the horizontal component of the velocity using the equation v_ix = v_i × cos(theta), where v_ix is the horizontal component of the initial velocity.
v_ix = 13 m/s × cos(32 degrees)
9. Finally, calculate the magnitude of the velocity at the highest point using the vertical and horizontal components. The magnitude of the velocity is given by the equation v_highest = sqrt(v_ix^2 + v_iy^2).
v_highest = sqrt(v_ix^2 + v_iy^2)
By following these steps and performing the calculations, you will find the speed of the ball at its highest point.