A ball thrown horizontally from a point 26.0 m above the ground strikes the ground after travelling a horizontal distance of 23.0 m. With what speed was it thrown?
Which equation should I use?
V= DeltaX / Delta T
A= Delta V / Delta T
Horizontal motion where X= Xo + Vx(T)
To find the initial speed at which the ball was thrown, you can use the equation of horizontal motion: X = Xo + VxT.
In this equation, X represents the horizontal distance traveled by the ball (23.0 m), Xo represents the initial horizontal position (0 m), Vx represents the horizontal velocity or the speed at which the ball was thrown (what we need to find), and T represents the time taken for the ball to travel the given distance.
Since the ball is thrown horizontally, the initial vertical velocity is zero. Thus, there is no vertical acceleration acting on the ball, and we can disregard vertical motion for this calculation.
Using the equation X = Xo + VxT, we can rearrange it as Vx = (X - Xo) / T.
Plugging in the given values, we have Vx = (23.0 m - 0 m) / T.
However, we still need to find the value of T, the time it took for the ball to travel the given distance. To do this, we can use the equation V = ΔX / ΔT, where V represents the vertical velocity or the initial speed at which the ball was thrown, ΔX represents the vertical distance (26.0 m), and ΔT represents the time taken.
Since the ball is only influenced by gravity in the vertical direction, we can use this equation to find the time taken, ΔT. Rearranging it, we have ΔT = ΔX / V.
Plugging in the given values, we have ΔT = 26.0 m / V.
Now we can substitute the expression for ΔT into the original equation for Vx: Vx = (23.0 m - 0 m) / (26.0 m / V).
Simplifying this further, we have Vx = (23.0 m * V) / 26.0 m.
Therefore, the equation you will ultimately use to find the initial speed at which the ball was thrown is:
Vx = (23.0 m * V) / 26.0 m.
To determine the speed at which the ball was thrown, you need to know the vertical distance the ball traveled or the vertical velocity at which it was thrown.