a man stand on a 100 m cliff and throws a rock with speed of 40ms at 42degrees above horizontal.
what time before rock hits ground.
the horizontal distance the rock traveled from base of cliff.?
my answer is 4.08 sec before rock hits ground
81.6 m distance traveled from base of cliff
The height of the rock above the base of the cliff is:
Y = 100 + 40 sin 42 t - 4.905 t^2
= 100 + 26.765 t - 4.905 t^2.
When t = 4.08, Y = 127 m
Your answer is incorrect.
Solve for t when Y = 0
Then multiply that time by 40 m/s*cos 42, the horizontal velocity component.
To find the time it takes for the rock to hit the ground, we can separate the horizontal and vertical components of its motion.
First, let's find the time of flight for the rock using its vertical motion. We can do this by calculating the time it takes for the rock to reach its highest point, and then double that time to find the total time of flight.
To calculate the time to reach the highest point, we use the following formula:
v_y = v_i * sin(theta)
where:
v_y is the vertical component of the initial velocity (initial velocity * sin(theta))
v_i is the initial velocity (40 m/s in this case)
theta is the launch angle (42 degrees)
v_y = 40 m/s * sin(42 degrees) ≈ 24.68 m/s
Next, we can calculate the time taken for the rock to reach its highest point using the vertical motion formula:
t = v_f / g
where:
t is the time taken (unknown)
v_f is the final vertical velocity (0 m/s at the highest point)
g is the acceleration due to gravity (9.8 m/s^2)
t = 24.68 m/s / 9.8 m/s^2 ≈ 2.52 seconds
To find the total time of flight, we multiply the time to reach the highest point by 2:
Total time of flight = 2 * 2.52 seconds ≈ 5.04 seconds
So the rock will hit the ground approximately 5.04 seconds after it was thrown.
To find the horizontal distance traveled by the rock from the base of the cliff, we use the horizontal component of its motion. The horizontal velocity remains constant throughout the motion.
To calculate the horizontal distance traveled, we use the following formula:
d = v_x * t
where:
d is the horizontal distance traveled (unknown)
v_x is the horizontal component of the initial velocity (initial velocity * cos(theta))
t is the time of flight (5.04 seconds)
v_x = 40 m/s * cos(42 degrees) ≈ 30.70 m/s
d = 30.70 m/s * 5.04 seconds ≈ 154.63 meters
Therefore, the rock will travel approximately 154.63 meters horizontally from the base of the cliff.