a car accidently roll offs cliff.As it leaves the cliffit has horizontal velocity of 13metre/second it hits the ground 60metre from the shore line to find the total time that the projectile hits the ground of cliff
time of flight = 60 m / 13 m/s
To find the total time that the projectile hits the ground, we can break down the problem into two separate motions: the horizontal motion and the vertical motion.
1. Horizontal Motion:
Since there are no horizontal forces acting on the object, its horizontal velocity remains constant throughout the motion. Therefore, the time taken to travel 60 meters horizontally can be found using the equation:
time = distance / velocity
Substituting the values, we have:
time = 60 meters / 13 meters/second
time ≈ 4.62 seconds
2. Vertical Motion:
Considering the vertical motion, we can use the equation of motion:
h = ut + (1/2)gt^2
Where:
h = vertical distance
u = initial vertical velocity (zero in this case as the car rolled off the cliff)
g = acceleration due to gravity (approximately 9.8 meters/second^2)
t = time
The car started at zero height, and the vertical distance it covers until it hits the ground is 60 meters. Thus, we can rewrite the equation as:
60 = 0 + (1/2)(9.8)t^2
Rearranging the equation, we get:
t = √(2h / g)
Substituting the values, we have:
t = √(2 * 60 meters / 9.8 meters/second^2)
t ≈ √12.24
t ≈ 3.49 seconds
Therefore, the total time it takes for the projectile to hit the ground is approximately 3.49 seconds.
To find the total time it takes for the car to hit the ground, we can use the equations of projectile motion. The horizontal velocity of the car, 13 meters/second, remains constant throughout the motion because no horizontal force is acting on it.
The vertical motion of the car can be described using the equation:
y = y0 + v0y * t + (1/2) * a * t^2
Where:
y is the vertical displacement (60 meters in this case)
y0 is the initial vertical displacement (0 meters since the car starts from the cliff)
v0y is the initial vertical velocity (unknown, since it is not given in the question)
a is the acceleration due to gravity (-9.8 m/s^2, assuming the motion occurs near the surface of the Earth)
t is the time it takes to hit the ground
Since we want to solve for t, we can rearrange the equation as follows:
y = (1/2) * a * t^2
Plugging in the known values, we get:
60 = (1/2) * (-9.8) * t^2
Simplifying, we have:
60 = -4.9 * t^2
Dividing both sides by -4.9, we get:
t^2 = -60 / -4.9
t^2 = 12.2449
Taking the square root of both sides, we find:
t ≈ √12.2449
t ≈ 3.5 seconds
Therefore, the total time it takes for the projectile (car) to hit the ground is approximately 3.5 seconds.