Find the height of a ball after 3 seconds, if the ball is hit with an initial velocity of 90 feet per second at an angle of 60 degrees from an initial height of 5 feet.
h(t) = 5 + (90 sin60°)t - 16t^2
Now just plug in t=3.
To find the height of the ball after 3 seconds, we need to break down the motion of the ball into horizontal and vertical components.
First, let's find the initial vertical velocity of the ball. We know that the initial velocity is 90 feet per second and it was hit at an angle of 60 degrees. The vertical component of the initial velocity can be found by multiplying the initial velocity by the sine of the launch angle:
Vertical component of initial velocity = 90 * sin(60 degrees)
Vertical component of initial velocity = 90 * 0.866
Vertical component of initial velocity ≈ 77.94 feet per second
Next, we can use this initial vertical velocity to find the height of the ball after 3 seconds. We can use the formula for vertical motion under gravity:
Height = Initial height + (Initial vertical velocity * time) - (0.5 * acceleration * time^2)
The acceleration due to gravity is approximately 32.2 feet per second squared. Plugging in the values, we have:
Height = 5 + (77.94 * 3) - (0.5 * 32.2 * (3^2))
Height ≈ 5 + 233.82 - (0.5 * 32.2 * 9)
Height ≈ 5 + 233.82 - 145.35
Height ≈ 93.47 feet
Therefore, the height of the ball after 3 seconds is approximately 93.47 feet.