Question

Mikalee, a fighter pilot, ejects from her burning plane. Once she is safely on the ground, she launches a flare to attract the attention of a rescue plane. The initial velocity of the flare is 1600 ft/sec.

What is the maximum height of the flare?

50 ft

400 ft

4,000 ft

40,000 ft

Answer 1

We can use the following equation from kinematics:
\[v_f ^2 = v_i ^2 + 2ad\]Where v_f and v_i are the final and initial velocities, a is acceleration due to gravity, and d is the distance. We're solving for the distance. When the flare is at its max height, its velocity is zero. So:
\[0=(1600 ft/s)^2 + 2(-32 f/s^2)d\]Now, solve for d. Can you try solving this on your own?

Answer 2

is there a more simple equation?

Answer 3

I believe this is as simple as you're going to get.

Answer 4

ok, can you take me step by step ?

Answer 5

Sure. We'll square the 1600 ft/s and multiply the 2 with the -32 ft/s^2 to get:
\[0=2560000 ft^2 / s^2 - (64 ft/s^2)d\]Now add 64d to both sides:
\[d(64 ft/s^2)=2560000 ft^2 / s^2\]Can you do the last step?

Answer 6

the answer is 40000?

Answer 7

Yes, exactly.

Answer 8

so if you were trying to find the maximum height of the flare would you ........

Answer 9

The most direct method is to use the kinematics formula I gave you above.