# Calculus

posted by Mike

A rocket follows a path given by y=x-1/91x^3 where distances are in miles. If the horizontal velocity is given by vx=1.4x, find the direction of the velocity when the rocket hits the ground (assume level terrain) if time is in minutes.

So far I've only taken the derivative for y and don't know what to do afterwards

Vx=1.4x
Vy=1-(3/91)x^2

1. Damon

Maybe you mean
y=x - (1/91) x^3
if so

y = 0 at ground, start and finish
0 = x - (1/91) x^3
x = 0 works of course
x^2 = 91
x = 9.54

Vx = 1.4 x = 13.4 miles/min at ground
what is Vy ?
dy/dt = dy/dx * dx/dt = [1-(3/91)x^2 ] Vx = [ 1-(3/91)9.54^2 ] 13.4 miles/min

## Similar Questions

1. ### physics

an airplane is diving at a speed of 300 km/h and the angle betweent he plane's dive path and the vertical is 50 degrees. The plane launches a rocket which lands at 750m horizontally from beneath the launch point. a) find the flight …
2. ### physics

It is possible for the velocity of a rocket to be greater than the exhaust velocity of the gases it ejects. When that is the case, the gas velocity and momentum are in the same direction as the rocket's. How does the rocket still obtain …
3. ### physics

A rocket is fired straight up and accelerates upward at 24 m/s2 for 12 seconds. The rocket then runs out of fuel and coasts. Ignore any air resistance effects and use -9.8 m/s2 for the local acceleration due to gravity. a) What is …
4. ### Calculus

Mathematica Project - Position, Velocity, and Acceleration?
5. ### physics

A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 79.0 m/s at ground level. The engines then fire, and the rocket accelerates upward at 3.90 m/s2 until it reaches an altitude of …
6. ### physics

A test rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 49 m and …
7. ### physics

A stationary rocket is launched vertically upward. After 4s, the rocket's fuel is used up and it is 225.6 m above the ground. At this instant the velocity of the rocket is 112,8 m/s. Then the rocket undergoes free fall. Ignore the …
8. ### math

a model rocket is projected straight upward from the ground level. It is fired with an initial velocity of 192 ft/s. How high is the rocket after 10 seconds?
9. ### Physical

A toy rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 73 m and acquired …
10. ### physics

A rocket is fired vertically and reaches a speed of 34.3 m/s in half a second. One and a half seconds later the rocketâ€™s speed is 19.6 m/s. Find the acceleration (in m/s2) and initial velocity (in m/s) of the rocket. Complete the …

More Similar Questions