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 A

Find the time tH it takes the projectile to reach its maximum height H.

Express tH in terms of v0, ?, and g (the magnitude of the acceleration due to gravity).

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.

Part C

Find H, the maximum height attained by the projectile.

Express your answer in terms of v0, ?, and g.

Part D

Find the total distance R (often called the range) traveled in the x direction; see the figure in the problem introduction.

Express the range in terms of v0, ?, and g.

Explanation / Answer

a)

tH = v0*sin(theta)/g

b)

tR = R/(v0*cos(theta))

c)

H = (V0*sin(theta))^2/(2g)

d)

R = 2*V0*cos(theta) * v0*sin(theta)/g

R = V0^2*sin(2*theta)/g

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