Physics Problem Solving.

Question

Two rackets are launched at a fireworks performance. Rocket A is launched with an initial velocity Vo and rocket B launched 4seconds later with the same initial velocity. The two rackets are timed to explode simultaneously at a height of 80meters, as A is falling and B is rising. Assuming a constant g=9.8m/s^2, determine (a)the initial velocity Vo, (b)the velocity of B relative to A at the time of the explotion.

Answer 1

First off, these are mortars, and not rockets or rackets.

The height of the first mortar is h = 0.5at² + vt

The height of the second mortar is h = 0.5a(t-4)² + v(t-4)

Now, plug in the constants:

80 = 0.5(-9.8)t² + V₀t = -4.9t² + V₀t

80 = 0.5(-9.8)(t-4)² + V₀(t-4) = -4.9(t²-8t+16) + V₀t - 4V₀

There are a number of ways you can solve for t here, but it's all algebra from here.