To understand how to apply the equations for one-dimensional motion to the x and

Question

To understand how to apply the equations for one-dimensional motion to the x and y directions separately in order to derive standard formulas for the range and height of a projectile.

(Figure 1) A projectile is fired from ground level at time t=0, at an angle ? with respect to the horizontal. It has an initial speed v0. In this problem we are assuming that the ground is level.

Part B

Find tR, the time at which the projectile hits the ground after having traveled through a horizontal distance R.

Express the time in terms of v0, ?, and g. (tR=?)

Note: R is not a known value there fore it can not be expressed in the answer.

Explanation / Answer

In the vertical direction, at the very top of the path, the velocity will momentarily be 0 m/s before it begins to fall back down.

We can find the time to travel upward to that stopping point.

The initial velocity in the vertical direction is vosin(theta)

Remembering the formula from one dimentional motion, we will use

vf = vo + at

vf = 0, vo = vosin(theta) and 'a' is gravity (g)

Thus 0 = vosin(theta) - gt

Solve for t...

t = vosin(theta)/g

That is the time to go up. It take the same amount of time to come back down, so multiply by 2..

tR = 2vosin(theta)/g

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