Solve the following word problem.

Question

The speed (in feet per second) of a ball tossed up in the air can be represented by the function v(t)=32|t|+5 where t is time in seconds. Based on this function, at what time would the speed of the ball be equal to 69 feet per second?

Answer 1

Rachel, 

 

If no other information is available, I will just have to solve two different problems.

 

(1)

 

Assume you toss up and the positive direction is up.

 

v(t) = -32t + 5

 

If you want 69 ft/s in the up direction, there is no solution, because there is no positive t that makes

 

69 = -32t + 5.

 

A negative t is not appropriate because t = 0 is the moment the ball is tossed up at an initial speed of 5 ft/s.  Before t=0, the ball was not in the state of motion described by the given equation.  However, it can reach 69 ft/s on the way down, which is a velocity of -69 ft/s.

 

-69 = -32t + 5 ⇒ t = (-69 - 5)/(-32) s = 2.31 s

 

(2)

 

Assume you toss down and the positive direction is down.

 

v(t) = 32t + 5

 

69 = 32t + 5

 

t = (69 - 5)/(32) s = 2s