A stunt motorcyclist is attempting to jump over a river of width 60m using a ramp which is inclined at 30 degrees to the horizontal. Assume the height of the ramp is small enough to be ignored in the calculations.
a) What is the minimum speed the stunt motorcyclist would need to jump over the river?
b) What it the maximum height above the river that the stunt motorcyclist reaches while jumping?
a. Range = Vo^2*sin(2A)/g = 60 m.
Vo^2*sin(60)/9.8 = 60
0.0884Vo^2 = 60
Vo^2 = 679
Vo = 26.06 m/s.[30o]
b. Yo = 26.06*sin30 = 13.03 m/s = Ver.
component.
hmax = (Y^2-Yo^2)/2g
hmax = (0-13.03^2)/-19.6 = 8.66 m.
To answer these questions, we can use the principles of projectile motion.
a) To find the minimum speed the stunt motorcyclist would need to jump over the river, we can use the horizontal component of the velocity. The horizontal component remains constant throughout the motion, so the motorcyclist should have enough horizontal velocity to cover the 60m distance. We can use the equation:
distance = velocity * time
In this case, the distance is 60m, and we can find the time by dividing the distance by the horizontal component of the velocity. So the equation becomes:
60m = V_horizontal * t
To find the horizontal component of velocity, we need to find the time of flight first. In projectile motion, the vertical motion follows a parabolic path, and the time of flight can be found using the equation:
time = (2 * vertical component of initial velocity) / gravitational acceleration
Since the ramp height can be ignored, the vertical component of the initial velocity is zero. So the time of flight would be:
time = (2 * 0) / gravitational acceleration = 0
The time value is zero because the vertical component of initial velocity is zero, meaning the motorcyclist does not spend any time in the air. Therefore, the horizontal component of velocity is simply:
V_horizontal = distance / time = 60m / 0 = undefined
In this case, it is not possible to calculate the horizontal component of velocity since the time is zero. Thus, the minimum speed required to jump over the river is undefined.
b) To find the maximum height above the river that the motorcyclist reaches while jumping, we need to find the vertical component of the velocity at the highest point. At the highest point of the trajectory, the vertical component of velocity becomes zero. This can be determined using the following equation:
final velocity^2 = initial velocity^2 - 2 * gravitational acceleration * height
Since the final velocity is zero at the highest point, the equation becomes:
0 = initial velocity^2 - 2 * gravitational acceleration * height
We can rearrange this equation to solve for the height:
height = (initial velocity^2) / (2 * gravitational acceleration)
Since we do not have the value of the initial velocity, we cannot calculate the maximum height reached by the motorcyclist without further information.