# Trajectory of a cyclist leaving a ramp

• pb23me
In summary, the motorcycle rider will not be able to jump over all 10 buses, but will be able to jump over most of them if the ramps are moved back to synchronize the horizontal and vertical motion.
pb23me

## Homework Statement

The problem says: A motorcycle daredevil is attempting to jump across 10 buses. The takeoff ramp makes an angle theta = 18 degrees above the horizontal, and the landing ramp is identical to the take off ramp. The buses are parked side by side and each bus is 2.74m wide. The cyclist leaves the ramp with a speed of v = 33.0. does he succeed in jumping over the buses? I am not sure how to go about solving this prob. It seems as though I am supposed to assume Yf=0 but i don't think i should?

Now my variables:
Xi : 0
Xf:?
Ax : 0 m/s^2
Vxi : 33.0(cos 18. degrees)
Vxf : 33.0(cos 18. degrees)
t : ?

Yi:0
Yf:?
Ay : ?
Vyf : ?
Vyi : 33.0(sin 18 degrees)
t : ?

## The Attempt at a Solution

Last edited:

Yes, I would assume assume Yf=0.
The height of the buses is not given, so I would assume the ramps are sufficiently high that the bike clears the first and last buses okay and the gap between ramps is just 10*2.74 meters.

You should be able to get the time of flight easily from the horizontal part of the motion.

why do you assume the bike hits the ramp at exactly the same y coordinate as when it took off? it seems to me you wouldn't really know that eg it hits much lower down the ramp.

find the y component velocity and see how long it takes to reduce vertical velocity to zero due to gravity. And you know that it takes the same amount of time to fall that same distance. Does horizontal velocity ever change? with knowing this you know how far it hits on the ground

no horizontal doesnt. and so your saying find time for the motorcycle to reach max height then multiply that time by two??

pb23me said:
no horizontal doesnt. and so your saying find time for the motorcycle to reach max height then multiply that time by two??

well you have to know why the vertical path has a total time of 2t.

but yes time is multiplied by 2

Sorry, I was thinking of a slightly different problem!
You are quite right, there is something missing from this question.
As it stands, the bike will cross the horizontal distance of 27.4 m in 0.873 seconds. In that time the vertical motion will be incomplete and the bike will be more than 6 meters above the launch point. If the ramps were moved back away from the buses to synchronize the horizontal and vertical motion, it could work. Question not clear?

Delphi51 said:
Sorry, I was thinking of a slightly different problem!
You are quite right, there is something missing from this question.
As it stands, the bike will cross the horizontal distance of 27.4 m in 0.873 seconds. In that time the vertical motion will be incomplete and the bike will be more than 6 meters above the launch point. If the ramps were moved back away from the buses to synchronize the horizontal and vertical motion, it could work. Question not clear?

technically it does not state he has to hit the landing ramp, it asks if he will jump all the buses

Good point! So the answer is very simple after all.
Kind of a wreck of a question, though.

## 1. How does the angle of the ramp affect the trajectory of the cyclist?

The angle of the ramp plays a crucial role in determining the trajectory of the cyclist. If the ramp is steeper, the cyclist will gain more height and cover less horizontal distance. On the other hand, a lower angle will result in a longer horizontal distance and lower height.

## 2. What is the impact of the cyclist's speed on their trajectory?

The speed of the cyclist also affects their trajectory. A higher speed will result in a longer jump and a shorter time in the air. This is because the horizontal velocity of the cyclist remains constant, while the vertical velocity increases with speed.

## 3. How does air resistance affect the trajectory of the cyclist?

Air resistance can have a significant impact on the trajectory of the cyclist. The higher the speed, the greater the air resistance, which can cause the cyclist to lose speed and height. This is why professional cyclists often adopt aerodynamic positions to reduce air resistance and improve their trajectory.

## 4. Can the weight of the cyclist affect their trajectory?

Yes, the weight of the cyclist can influence their trajectory. A heavier cyclist will have a greater downward force due to gravity, resulting in a shorter jump and lower trajectory. However, the weight of the cyclist may not have a significant impact if they have a high-speed and the ramp is steep enough.

## 5. What other factors can affect the trajectory of a cyclist leaving a ramp?

Apart from the angle of the ramp, speed, air resistance, and weight, other factors that can affect the trajectory of a cyclist include the shape and condition of the ramp, the force applied by the cyclist, and external forces such as wind or friction. The cyclist's balance and technique can also play a role in determining their trajectory.

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