A catapult on a cliff launches a large round rock towards a ship on the ocean below. The rock leaves the catapult from a height H = 35.0 m above sea level, directed at an angle theta = 46.7° above the horizontal, and with a speed v = 28.4 m/s. Assuming that air friction can be neglected, calculate the horizontal distance D traveled by the projectile.

Question

A catapult on a cliff launches a large round rock towards a ship on the ocean below. The rock leaves the catapult from a height H = 35.0 m above sea level, directed at an angle theta = 46.7° above the horizontal, and with a speed v = 28.4 m/s. Assuming that air friction can be neglected, calculate the horizontal distance D traveled by the projectile.

Could someone give me the first step? I know that I will eventually use delta x = vx x t, but what do I need to do before that?

Answer 1

The first step is the vertical equation, to determine the time in air.

Determine the vertical and horizontal components of the initial velocity.

Vertical equation.

Hfinal=Hinitial + Viv*t - 1/2 g t^2

solve for t, the time in air. Then work the horizontal equation.

dfinal=vih*t

Answer 2

Height reached above the cliff is h = V^2sin^2(µ)/9.8.

t1 = Vsin(µ)/9.8.

h + 35 = 9.8t2^2/2---->t2

d = Vcos(µ)(t1 + t2)

Answer 3

Well, before you can use that equation, you need to determine the time it takes for the projectile to hit the target. To do that, you can break the initial velocity into its horizontal and vertical components.

The horizontal component of the velocity (v_x) is given by v_x = v * cos(theta), and the vertical component (v_y) is given by v_y = v * sin(theta).

Once you have the vertical component, you can use the equation h = v_y * t - (1/2) * g * t^2 to find the time (t) it takes for the rock to reach the ocean below. Here, h is the initial height of the rock above sea level (H), and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Once you have the value of t, you can then use the horizontal component of velocity (v_x) and the time (t) to calculate the horizontal distance traveled (delta x) using the equation delta x = v_x * t.

Answer 4

To calculate the horizontal distance traveled by the projectile, we can break the initial velocity into its horizontal and vertical components. The horizontal component of the velocity (Vx) remains constant throughout the motion, while the vertical component changes due to the effect of gravity.

To find the horizontal component of the velocity, we use the equation:
Vx = V * cos(theta)

Substituting the given values, we have:
Vx = 28.4 m/s * cos(46.7°)

Now, you can calculate the value of Vx.

The first step is the vertical equation, to determine the time in air.

Thanks!

Height reached above the cliff is h = V^2sin^2(µ)/9.8.

Well, before you can use that equation, you need to determine the time it takes for the projectile to hit the target. To do that, you can break the initial velocity into its horizontal and vertical components.

To calculate the horizontal distance traveled by the projectile, we can break the initial velocity into its horizontal and vertical components. The horizontal component of the velocity (Vx) remains constant throughout the motion, while the vertical component changes due to the effect of gravity.