physics:a train exploded & a 50kg wheel flew 250m high landing 2km away,what was the wheel's velocity & angle

Question

this is a physics problem that i cant figure out, i dont necessarily need the answer, just the formula i can use to solve it.

Answer 1

First, you can ignore the mass of the wheel, since any object of any mass would follow the same path at the same speeds ... as long as you ignore air resistance. (If you have to consider air resistance, this is a very advanced problem, and I don't think that's what you're being asked to do.)

OK. If it went 250 m in the air, you can calculate the time of the flight by using the formula for distance fallen under the force of gravity: dist = (g t^2) / 2
In this case, 250 m = (9.8 m/s^2) (t^2) / 2
Solving, t = 7.143 sec

That's the time to fall from 250 m.
And it's also the time to rise to 250 m (if the vertical velocity is 0 at 250 m).
So we have to double it to get the total time of the flight:
14.286 sec.

The object went 2 km horizontally in 14.286 sec, so it was travelling at a (constant) horizontal velocity of
2000 m / 14.286 sec = 140 m/sec.

Now we have to find the initial vertical velocity. since we know the vertical will drop to 0 in 14.286 seconds, being decelerated at 9.8 m/sec^2, its initial vertical velocity is
14.286 sec x 9.8 m/sec^2 = 140 m/sec.

Conveniently, the vertical velocity is equal to the horizontal velocity, so we know that the tangent of the angle is 1, which means that the angle is 45 degrees (or pi/4, if you prefer radians).

Answer 2

This is a projectile question mixed with energy.

You'll need to look at the x-direction and y-direction
in the x-direction the equation of motion is

x=v*cos(θ)*t (I)

in y-direction
y=v*sin(θ)*t-(1/2)gt^2 (II)

combining and eliminating t

y=tan(θ)x-g/(2v^2cos^2(θ))*x^2 (III)

The maximum height is v^2(sin(θ))^2/(2g) (IV)

using energy consideration v=sqrt(2gh) (V)

so plugging in

putting it together,

Use equation (V) to find the velocity v, then use the height (given) and the velocity v (derived) with equation (IV) to get the angle θ. Interestingly, you really don't need to know the mass.

Answer 3

The weight of the wheel isn't important. You can probably find the formula you need here: