Question

An object dropped from a height of 600 feet has a height, h(t), in feet after t seconds have elapsed, such that h(t)=600 - 16t^2. Express t as a function of height h, and find the time to reach a heigh of 50 feet

Answer 1

Answer:

t as a function of height h is  t = √600 - h/16

The time to reach a height of 50 feet is 5.86 minutes

Step-by-step explanation:

Function for height is h(t) = 600 - 16t²

where t = time lapsed in seconds after an object is dropped from height of 600 feet

t  as a function of height h

replacing the function with variable h

h = 600 - 16t²

Solving for t

Subtracting 600 from both side

h - 600 = -16t²

Divide through by -16

600 - h/ 16 = t²

Take square root of both sides

√600 - h/16 = t

Therefore, t = √600 - h/16

Time to reach height 50 feet

t = √600 - h/16

substituting h = 50 in the equation

t = √600 - 50/16

t = √550/16

t= 34.375

t = 5.86 minutes