Question

for exercises 9 and 10, use the formula h(t)=v_0t - 16t^2, where h(t) is the height of an object in feet, v_0 is the objects initial velocity in feet per second, and t is the time in seconds. 9. baseball marta throws a baseball with an initial upward velocity of 60 feet per second. ignoring martas height, how long after she releases the ball will it hit the ground?

Explanation:

Step1: Set up the equation

When the ball hits the ground, $h(t)=0$. Given $v_0 = 60$ and the formula $h(t)=v_0t - 16t^{2}$, we substitute to get $0 = 60t-16t^{2}$.

Step2: Factor the equation

Factor out a common factor of $t$: $0=t(60 - 16t)$.

Step3: Solve for $t$

Set each factor equal to zero. First, $t = 0$ represents the time of release. For the other factor, $60-16t=0$. Then $16t=60$, so $t=\frac{60}{16}=\frac{15}{4}=3.75$ seconds.

Answer:

$3.75$ seconds