Projectile motion motorcycle jump over cliff

In summary, a motorcyclist jumps off a cliff inclined at 53.0 degrees over a river that is 40.0m wide. The far bank is 15.0m lower than the edge of the take off ramp. The river itself is 100m below the ramp. Ignore air resistance. What should his speed be at the top of the ramp to just make it to the edge of the far bank?
  • #1
offbeatjumi
28
0
a motorcyclist jumps off a cliff inclined at 53.0 degrees over a river that is 40.0m wide. the far bank is 15.0m lower than the edge of the take off ramp. the river itself is 100m below the ramp. Ignore air resistance. What should his speed be at the top of the ramp to just make it to the edge of the far bank?

given:
theta = 53.0 deg.
d = 40.0 m
change(y) = 15.0 m

I'm just not sure what equation of projectile motion to use. Time is not really a factor in this... and I am confused because the variable t is in all the equations and where I don't know initial velocity, it leaves me with two unknown variables. Can someone just point me in the right direction, help me figure out which equations to use. Thank you so much.
 
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  • #2
offbeatjumi said:
a motorcyclist jumps off a cliff inclined at 53.0 degrees over a river that is 40.0m wide. the far bank is 15.0m lower than the edge of the take off ramp. the river itself is 100m below the ramp. Ignore air resistance. What should his speed be at the top of the ramp to just make it to the edge of the far bank?

given:
theta = 53.0 deg.
d = 40.0 m
change(y) = 15.0 m

I'm just not sure what equation of projectile motion to use. Time is not really a factor in this... and I am confused because the variable t is in all the equations and where I don't know initial velocity, it leaves me with two unknown variables. Can someone just point me in the right direction, help me figure out which equations to use. Thank you so much.

You end up with two simultaneous equations, so you can solve for both unknowns. One equation is for the horizontal motion, which has a constant velocity. The other equation is for the vertical motion as a function of time, and has a parabolic term in it due to the constant acceleration of gravity changing the vertical velocity as a function of time. Does that help?
 
  • #3
so i use x(t) = v(x)t + x(0) and the other equation is y = y(0) + v(0y)t - 1/2gt^2 ? even when i substitute known variables into these i have no idea what to do with them
 
  • #4
offbeatjumi said:
so i use x(t) = v(x)t + x(0) and the other equation is y = y(0) + v(0y)t - 1/2gt^2 ? even when i substitute known variables into these i have no idea what to do with them

You should clean up those starting equations a bit first. The velocity in the first equation should be v(t), for example, not v(x) (Quiz Question -- how come?). And you should be more explicit about the components to avoid what you are writing in the second equation "V(0Y)t" is confusing and potentially wrong. Try using Vx(t) and Vy(t) for the velocity names.

Now, you *do* have starting and ending coordinates, and and starting Vx(0) and Vy(0) values. Start writing those equations...
 

FAQ: Projectile motion motorcycle jump over cliff

How does the motorcycle maintain its momentum during the jump?

The motorcycle maintains its momentum through the principle of inertia, which states that an object in motion will continue moving at a constant speed and direction unless acted upon by an external force. In this case, the motorcycle's engine and wheels provide the necessary force to keep it moving forward as it jumps over the cliff.

How is the trajectory of the motorcycle calculated?

The trajectory of the motorcycle can be calculated using the equations of projectile motion, which take into account the initial velocity, angle of launch, and gravity. By plugging in these values, the path of the motorcycle can be determined and the rider can adjust their speed and angle accordingly.

What factors affect the distance the motorcycle can jump?

The distance the motorcycle can jump is affected by several factors, including the speed of the motorcycle, the angle of launch, and the height of the cliff. Additionally, external factors such as wind resistance and the weight of the rider and motorcycle can also impact the distance of the jump.

How does the rider ensure a safe landing after the jump?

The rider must carefully time their release from the motorcycle to ensure a safe landing. They must also take into consideration the angle of the cliff and the angle of the motorcycle's trajectory to ensure a smooth and controlled descent. Protective gear, such as a helmet and padding, can also help prevent injuries upon landing.

What are the potential risks of attempting a motorcycle jump over a cliff?

The potential risks of attempting a motorcycle jump over a cliff include serious injury or death to the rider if the jump is not executed properly. Other risks include damage to the motorcycle and potential harm to any bystanders or property in the vicinity of the jump. It is important for the rider to thoroughly assess and prepare for these risks before attempting the jump.

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