You throw a ball straight into the air from a height of 4 feet and with a speed of 5.3 m/s. The moment the ball leaves your hand you start running away at a speed of 2.37 m/s. How far are you from the ball, the moment it hits the ground?
4 feet =1.2192meters
(type **** 4 feet = meters ****into Google search box)
h = Hi + Vi t -4.9 t^2
0 = 1.22 + 5.3 t - 4.9 t^2
or
4.9 t^2 - 5.3 t -1.22 = 0
solve quadratic
t = [ 5.3 +/- sqrt (28.1+23.9) ]/9.8
use far answer
t = 1.28 seconds
1.28 * 2.37 = 3.03 meters
To find the distance between you and the ball when it hits the ground, we can break down the problem into two parts: the time it takes for the ball to reach the ground, and the distance you travel during that time.
First, let's find the time it takes for the ball to hit the ground. We know the initial height of the ball is 4 feet, and the only force acting on the ball is gravity. The formula to calculate the time it takes for an object to fall from a certain height is:
time = sqrt((2 * height) / g)
Where "g" is the acceleration due to gravity, which is approximately equal to 9.8 m/s^2.
Converting the initial height from feet to meters, we have:
height = 4 feet * (0.3048 m / 1 foot) = 1.2192 meters
Plugging in the values, we get:
time = sqrt((2 * 1.2192) / 9.8) ≈ 0.5 seconds
So it takes approximately 0.5 seconds for the ball to hit the ground.
Next, let's calculate the distance you travel during that time. You start running away from the ball at a speed of 2.37 m/s, and the time it takes for the ball to hit the ground is 0.5 seconds.
distance = speed * time
distance = 2.37 m/s * 0.5 s = 1.185 meters
Therefore, you would be approximately 1.185 meters away from the ball at the moment it hits the ground.