two students want to determine the speed at which a ball is released when thrown vertically upward into the air. one student throws the ball into the air while the other student measures the total time that the ball is in the air. the students use a meterstick to measure the release height of the ball. which of the following equations should the students use to determine the speed at which the ball was released?
Which equation should the students use to determine the speed at which the ball was released?
Answer:
To determine the speed at which the ball was released when thrown vertically upward, the students should use the kinematic equation for vertical motion. The equation that relates the initial velocity, final velocity, acceleration, and displacement in vertical motion is:
v_f^2 = v_i^2 + 2a \cdot \Delta y
Where:
- ( v_f ) is the final velocity (which in this case is 0 m/s at the highest point of the ball’s trajectory),
- ( v_i ) is the initial velocity (the speed at which the ball was released),
- ( a ) is the acceleration due to gravity (approximately -9.81 m/s²),
- ( \Delta y ) is the displacement in the vertical direction.
Given that the final velocity at the highest point is 0 m/s, the equation can be simplified to:
0 = v_i^2 + 2a \cdot \Delta y
The initial velocity can then be calculated using the measured values of the total time the ball is in the air and the release height of the ball.