A bullet is fired upward reaches maximum height of 2500m. find out how long it would have taken to reach the height of 2500m

Question

 This is a numerical of physics which i cant solve so please help mee

Answer 1

Assuming the bullet was fired from the ground, we need to solve for t in the equation

 

-4.9t² + vt = 2500 m

 

But we first need to find the initial speed v, as Sean pointed out.  We can find v from kinematics.

 

v_f² - v² = 2ah_max

 

v_f = 0  [instantaneous rest at h_max]

v = initial speed = ?  [what we want to find]

a = -g = -9.8 m/s²

h_max = 2500 m

 

v = √(2gh_max) = √[2(9.8)(2500)] m/s ≅ √(49,000) m/s

 

Then

 

h(t) = -4.9t² + [√(49,000)]t

 

with h in meters, t in seconds.

 

Now set h = 2500 m and solve for t. 

 

2500 = -4.9t² + [√(49,000)]t

 

-4.9t² + [√(49,000)]t - 2500 = 0

 

You now have a quadratic equation in t, which you should know how to solve, and get

 

t ≅ 22.59 seconds.