Question

question 13 of 20
the equation for a projectiles height versus time is ( h(t) = -16t^2 + v_0 t + h_0 ). a ball is thrown vertically upward with an initial velocity of 2 ft/sec from a height of 6 feet. which function models its motion?

a. ( v = 16t^2 - 2t - 6 )

b. ( v = -16t^2 + 6t + 2 )

c. ( v = -16t^2 - 6t - 2 )

d. ( v = -16t^2 + 2t + 6 )

Explanation:

Step1: Identify given values

We know the height function is \( h(t) = -16t^2 + v_0t + h_0 \). Here, initial velocity \( v_0 = 2 \) ft/sec and initial height \( h_0 = 6 \) feet.

Step2: Substitute values into the formula

Substitute \( v_0 = 2 \) and \( h_0 = 6 \) into \( h(t) \) (note that the function is about height, but the options use \( v \) which should be a typo for \( h \)). So \( h(t)=-16t^2 + 2t + 6 \).

Answer:

D. \( v = -16t^2 + 2t + 6 \)