Physics help! if you can answer any of the following questions or all, that would be great, give explanation?

Question

plz show as many steps as possible, i need serious help in physics, thank you so much to everyone!

1)A rock is thrown with a velocity of 11.2m/s, and has an angle 15 degrees from horizontal from the top of a cliff which is 42.5m high a) how long airborne? B) calculate range

2) Plane flied west from Toronto to Edmonton at a speed of 789 km/h (with respect to air) a) find the direction the plane should have to compensate for wind with velocity of 56.3 km/h north b( find the speed of plane relative to ground

3) Object A exerts a gravitational force of magnitude 1.3 * 10^-10 N on object B. what is magnitude of gravitational force if r is doubled, mass of object A is * 6, and mass of object B is halved

4) Determine max speed at which 1500 kg car can round a curve that has a radius = 40m, if miew = 0.6

Answer 1

I'll give you #1:

Consider the vertical (time) and horizontal (range) parts seperately. Start with the vertical...

To find the time for the rock to hit the ground, use

Y = 1/2 * a * t^2 + Vo * t + Yo

Sign convention is important here; there's more than one way to set it up, but here's how I did it:

Elevation at top of the cliff (Yo=0m)

Elevation of the ground below (Y=-42.5m)

the Y component of inital velocity is

Vyo = 11.2 * sin(15) = +2.9 m/s

accelleration in the y direction is just g = -9.8 m/s^2

so put all this into the equation and you get:

-42.5 = 1/2 * (-9.8) * t^2 + 2.9 * t + 0

which can be simplifed to:

t^2 - 0.59 * t - 8.67 = 0;

use quadratic equation (and take the root that yields a positive time...) and I get

t=3.25 sec.

This is the time for the rock to hit the ground.

This is also the time the rock has to reach it's final range, so

X = V * t, where the x component of velocity is constant

Vx = 11.2 * cos(15) = 10.8 m/s, so

Range = 10.8 * 3.25 = 35.2 m