Question

15 fill in the blank 12 points
if an object is shot upward with an initial velocity ( v_0 ) in feet per second, the velocity ( v ) in feet per second is given by the formula ( v = v_0 - 32t ), where ( t ) is the time in seconds. (( v_0 ) is read \v sub zero.\)
a) if an object projected upward with an initial velocity of 106 feet per second has a velocity of 42 feet per second, then how many seconds have passed?
seconds
b) find the initial velocity of an object if the velocity after 4 seconds is 48 feet per second.
feet per second

Explanation:

Step1: Substitute values into formula

Given \( v = v_0 - 32t \), \( v_0 = 106 \), \( v = 42 \). So \( 42 = 106 - 32t \).

Step2: Solve for t

Rearrange: \( 32t = 106 - 42 = 64 \). Then \( t = \frac{64}{32} = 2 \).

Step3: Substitute values for part b

Given \( t = 4 \), \( v = 48 \). So \( 48 = v_0 - 32(4) \).

Step4: Solve for \( v_0 \)

Calculate \( 32(4) = 128 \). Then \( v_0 = 48 + 128 = 176 \).

Answer:

a) 2
b) 176