You throw a ball straight into the air from a height of 4 feet and with a speed of 8.22 m/s. The moment the ball leaves your hand you start running away at a speed of 3.36 m/s. How far are you from the ball, the moment it hits the ground?
V = Vo + g*Tr = 0 at max ht.
8.22 - 9.8Tr = 0
9.8Tr = 8.22
Tr = 0.84 s. = Rise time or time to reach max ht.
hmax = ho + Vo*t + 0.5g*t^2
hmax=13.2 + 8.22*0.84 - 4.9*0.84^2=16.7 m. Above gnd.
0.5g*t^2 = 16.7 m.
4.9t^2 = 16.7
t^2 = 3.40
Tf = 1.84 s. = Fall time.
d = 3.36m/s * (0.84+1.84)s = 9.0 m.
Correction: 4 Ft = 1.21 m. Not 13.2 m.
hmax=1.21+8.22*0.84 - 4.9*0.84^2=4.66 m
Above gnd.
0.5g*t^2 = 4.66 m.
4.9t^2 = 4.66
t^2 = 0.95
Tf = 0.97 s. = Fall time.
d = 3.36m/s * (0.84+0.97) = 6.1 m.
To find the distance from the ball the moment it hits the ground, we need to determine how long it takes for the ball to reach the ground and then calculate the distance you have covered in that time.
First, let's determine the time it takes for the ball to reach the ground. We can use the equation of motion for vertical motion:
h = (vi * t) + (0.5 * g * t^2)
where:
h = initial height = 4 feet = 1.22 meters
vi = initial vertical velocity = 8.22 m/s (upward)
g = acceleration due to gravity = 9.8 m/s^2 (downward)
t = time
Since the ball will reach the ground when the height h becomes zero, we can rewrite the equation as:
0 = (8.22 * t) + (0.5 * 9.8 * t^2)
Simplifying the equation, we have:
4.9t^2 + 8.22t = 0
Now we can solve this quadratic equation for the positive value of t. By factoring or using the quadratic formula, we find that:
t = 0 or t = -8.22/4.9
Since time can't be negative, we take t = 0 as the initial condition, and we find that the time it takes for the ball to reach the ground is t = 0 seconds.
Now, let's calculate the distance you have covered in that time. Since you start running away at a speed of 3.36 m/s, the distance you have covered when the ball hits the ground is:
distance = velocity * time
= 3.36 m/s * t
= 3.36 m/s * 0 s
= 0 meters
Therefore, you are 0 meters away from the ball when it hits the ground.