a man stands on the roof of a 15.0m tall building and throws a rock with a velocity of magnitude 30.0m/s at an angle of 33 degrees above the horizontal. ignoring resistance calculate the horizontal distance from the base of the building to the point where the rock strikes the ground.
Given
v=30 m/s
θ=33°
h=15m
g=9.8 m/s²
Resolve velocity into horizontal (vx) ad vertical (vy) components,
vy=v*sin(θ)= 16.34 m/s
vx=v*cos(θ)= 25.16 m/s
Find time t to reach ground h m below:
y=vy*t+(1/2)at²
-15=16.34t-4.9t²
=>
4.9t²-16.34t-15=0
t=4.084 s (reject negative root)
Calculate horizontal distance
x=vx*t
= 25.16*4.084
= 102.8 m (approx.)
To calculate the horizontal distance from the base of the building to the point where the rock strikes the ground, we need to use the equations of motion.
First, we need to split the initial velocity of the rock into its horizontal and vertical components. The horizontal component of the velocity can be found using the equation:
Vx = V * cos(theta)
where V is the magnitude of the velocity (30.0 m/s) and theta is the angle above the horizontal (33 degrees).
Vx = 30.0 * cos(33)
Next, we can calculate the time it takes for the rock to hit the ground. To do this, we need to find the time it takes for the rock to reach its maximum height and then double that time to find the total time of flight.
The time it takes for the rock to reach its maximum height (t1) can be found using the equation:
t1 = Vy / g
where Vy is the vertical component of the velocity and g is the acceleration due to gravity (9.8 m/s^2).
To find Vy, we use the equation:
Vy = V * sin(theta)
Vy = 30.0 * sin(33)
Now we can calculate the time of flight (t) by doubling t1:
t = 2 * t1
Next, we can find the horizontal distance traveled by the rock using the equation:
Horizontal distance = Vx * t
Plug in the values we've calculated:
Horizontal distance = (30.0 * cos(33)) * (2 * (30.0 * sin(33)) / 9.8)
Simplifying this expression will give us the answer.