A Car Accidently Rolls Off A Cliff. As It Leaves The Cliff It Has A Horizontal Velocity Of 13 M/s, It Hits The Groung 60 M From The Shoreline. Calculate The Height Of The Cliff?
I guess it is high tide so the water reaches the cliff.
Well, there is a constant horizontal speed, call it u=13 m/s
so
13 t = 60 (that is a serious cliff !)
t = 60/13 = 4.615 seconds falling
well
h = Hi + Vi t - 4.9 t^2
Hi is what we want
Vi is initial vertical speed up = 0
4.9 = g/2
h = 0, bleak ocean height
0 = Hi + 0 - 4.9 t^2
Hi = 104 meters, yikes
To calculate the height of the cliff, we can use the equations of motion and the information given:
1. We are given the horizontal velocity of the car as it leaves the cliff, which is 13 m/s. Let's call this velocity "v".
2. The horizontal distance from the shoreline, where the car hits the ground, is given as 60 meters. Let's call this distance "d".
3. We know that the horizontal motion is independent of the vertical motion, so the time it takes for the car to travel the horizontal distance d is the same as the time it takes to fall vertically from the height of the cliff.
Now, we need to find the time it takes for the car to reach the ground. We can use the equation for horizontal motion:
d = v * t
where d is the horizontal distance (60 m), v is the horizontal velocity (13 m/s), and t is the time.
Rearranging the equation, we can solve for the time t:
t = d / v
= 60 m / 13 m/s
≈ 4.615 seconds
Now, we can determine the vertical distance traveled by the car during this time. We can use the equation for vertical motion:
h = (1/2) * g * t^2
where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Substituting the values, we get:
h = (1/2) * 9.8 m/s^2 * (4.615 s)^2
= 107.26 meters (rounded to two decimal places)
Therefore, the height of the cliff is approximately 107.26 meters.