Math Problem

Question

A bat, the flying kind, has a rocket strapped to its back. The bat is launched straight up. After 5 seconds, it is 500 ft above the ground. After 10 seconds it is 750 ft above the ground. 

 

 

a.) Assuming the rocket is propelling the bat at a constant speed, create a function that represents the bats height, h, after t seconds

 

 

 

b.) Verbally interpret the slope

Answer 1

f(5) = 500

f(10) = 750

 

f(t) is the displacement function, getting the 1st derivative will give you the velocity function. f'(t) = c₁ (constant as stated)

 

Integrating it back again will return you to the displacement function but it will now be: f(t) = c₁t + c₂ (the new constant is due to integration)

 

Using system of equations:

500 = c₁(5) + c₂

750 = c₁(10) + c₂

 

which will give you c₁ = 50 and c₂ = 250.

 

Therefore, your function will be f(t) = 50t + 250.