A football player kicks the ball with an initial upward velocity of 60 feet per second. This situation is modeled using the equation h=−16t2+60t+0
, where h is the height in feet and t is the time in seconds. Using this equation, what is the maximum range the ball will reach? Round to the nearest hundredth
The range of the ball is the horizontal distance it travels. Since the equation only represents the height, we need to find the time at which the ball hits the ground.
To find this, we set h = 0 and solve for t:
0 = -16t^2 + 60t
Divide both sides by -4t:
0 = 4t - 15
Solving for t gives:
t = 15/4 = 3.75 seconds
Now that we know the time at which the ball hits the ground, we can find the range. The range is the horizontal distance traveled at this time.
To find the range, we need to find the horizontal component of the velocity, as the vertical component does not affect the range.
Given that the initial velocity is 60 feet per second, we assume it is purely horizontal.
Therefore, the range is given by the formula:
R = V0 * t
where V0 is the initial horizontal velocity and t is the time at which the ball hits the ground.
In this case, the range is:
R = 60 * 3.75 = 225 feet
Therefore, the maximum range the ball will reach is 225 feet.