A tennis ball is launched with an initial velocity of 24.5 m/s from the edge of a cliff that is 117.6 meters above the ground. Which quadratic equation could be used to correctly determine when the ball will hit the ground
To determine when the ball will hit the ground, we can use the equations of motion. The equation that relates the height (h) of an object to its initial velocity (v0), acceleration due to gravity (g), and time (t) can be given as:
h = v0t - (1/2)gt^2
In this case, the initial velocity is 24.5 m/s and the acceleration due to gravity is approximately 9.8 m/s^2. The height of the cliff is 117.6 meters.
When the ball hits the ground, its height is zero. Therefore, we can set h = 0 and solve for t:
0 = v0t - (1/2)gt^2
Now, let's substitute the given values into this equation:
0 = 24.5t - (1/2)(9.8)t^2
Simplifying, we get:
0 = 24.5t - 4.9t^2
This is the quadratic equation that could be used to determine when the ball will hit the ground:
4.9t^2 - 24.5t = 0
To determine when the tennis ball will hit the ground, we can use the kinematic equation for vertical motion:
h = h_0 + v_0*t + (1/2) * a * t^2
Where:
h is the height of the ball above the ground,
h_0 is the initial height of the ball,
v_0 is the initial vertical velocity of the ball,
a is the acceleration due to gravity (approximately -9.8 m/s^2),
t is the time elapsed.
In this case, the initial height of the ball above the ground (h_0) is 117.6 m, and the initial vertical velocity (v_0) is -24.5 m/s (negative because the ball is launched upwards).
By substituting the known values into the equation, we get:
h = 117.6 + (-24.5) * t + (1/2) * (-9.8) * t^2
Simplifying this equation gives us:
h = -4.9 * t^2 - 24.5 * t + 117.6
Therefore, the quadratic equation that could be used to correctly determine when the ball will hit the ground is:
-4.9 * t^2 - 24.5 * t + 117.6 = 0