# math

posted by .

A projectile is launched from ground level to the top of a cliff which is 195m away and 135m high. If the projectile lands on top of the cliff 6.9s after it is fired, find the initial velocity of the projectile ((a)magnitude and (b)direction. Neglect air resistance.

• math -

The horizontal-component, ux, of the initial velocity is the horizontal distance (195m) divided by 6.9s.
The vertical component, uy, can be found by the equation:
S = uy t + (1/2)(-g)t²
where
S is the vertical distance of the target (135 m)
uy = vertical component of velocity
t = 6.9 seconds
g = acceleration due to gravity (9.81 m/s/s/)
from which uy can be found.

The direction is atan2(uy,ux) from the horizontal.

• math -

I don't understand how to get the magnitude. Do you just add the two numbers together?

What do you do to the angle if it asks for the angle below the positive x-axis?

• math -

You can obtain the magnitude by doing a vectorial sum, namely magnitude=√(ux²+uy²)

The direction from the x-axis is obtained from tan-1(uy/ux), which goes from -π/2 to +%pi/2. Since the angle could range from 0 to 2π, it is necessary to observe the sign of ux and uy and determine the quadrant accordingly.

For the given question, the angle should be above the horizon (x-axis). If it is below, it will never reach the top of the cliff, and the solution is not correct.

If another questions requires a solution
below the x-axis, the angle will be negative between 0 and π/2.

## Similar Questions

1. ### Physics

a) A cannonball is fired horizontally from the top of a cliff. The cannon is at height H = 100 m above ground level, and the ball is fired with initial horizontal speed v_0. Assume acceleration due to gravity to be g = 9.80 m/s^2. …
2. ### physics

projectile is launched horizontally from edge of cliff 20 m high with an initial speed of 10 m/s. what is the horizontal distance the projectile travels before striking the level ground below the cliff?
3. ### Physics

A projectile is launched from ground level to the top of a cliff which is 195m away and 135m high (as shown in the figure ).If the projectile lands on top of the cliff 6.9s after it is fired, find the initial velocity of the projectile …
4. ### Physics

A projectile is launched from ground level to the top of a cliff which is 195 m away and 155 m high. If the projectile lands on top of the cliff 9.2 s after it is fired, find the initial velocity of the projectile (magnitude and direction). …
5. ### physics

A projectile is launched from ground level to the top of a cliff which is 195 m away and 155 m high. If the projectile lands on top of the cliff 9.2 s after it is fired, find the initial velocity of the projectile (magnitude and direction). …
6. ### Physics

A projectile is launched from ground level to the top of a cliff which is 195 m away and 155 m high. If the projectile lands on top of the cliff 9.2 s after it is fired, find the initial velocity of the projectile (magnitude and direction). …
7. ### physics

A projectile is launched from ground level to the top of a cliff which is 195 m away and 135 m high.If the projectile lands on top of the cliff 6.5 s after it is fired, find the initial velocity of the projectile ( (a)magnitude and …
8. ### physics

A projectile is launched from ground level to the top of a cliff which is 195 m away and 135 m high.If the projectile lands on top of the cliff 6.5 s after it is fired, find the initial velocity of the projectile ( (a)magnitude and …
9. ### physics

A projectile is fired at an angle of 30ᵒ above the horizontal from the top of the cliff 600 ft high. The initial speed of the projectile is 2000 ft/s. how far will the projectile move horizontally before it hits the level ground …
10. ### physics

a projectile is fired at an angle of 27 above the horizontal from the top of a cliff 500 ft high. The initial speed of projectile is 1670 ft/s. How far will it move horizontally before hitting the level ground at the base of the cliff?

More Similar Questions

Post a New Question