Kinematics Problem (Find Speed)

[airking95]

Homework Statement

A daredevil motorcyclist attempts to leap a 48m wide gorge. At the side where the cyclist starts, the ground slopes upward at an angle of 15 degrees. Beyond the far rim, the ground is level and is 5.9m below the near rim. what is the minimum speed necessary for the cyclist to clear the gorge?

Homework Equations

Kinematics Equations

s=d/t
d= vf(t)-0.5(a)(t)2

The Attempt at a Solution

First I just used Pythagorean therm to find Δd. 48²+5.9²= c²

c= 48.36

Used equation to find time

Δd = V_fΔt-0.5(a)Δt²
48.36= -0.5(-9.8)Δt²
48.36 = 4.9Δt²
48.36/4.9=Δt²
9.86 =Δt²
+ - 3.14 = Δt

s=d/t
s=48.36/3.14
s=15.4 m/s

I think I was suppose to do something with 15 degrees.

I got the answer as 15 m/s, but I believe its wrong.

 

[azizlwl]

Maybe you show us your workings and if we can spot any errors you might have made.

 

[airking95]

Maybe you show us your workings and if we can spot any errors you might have made.

First I just used Pythagorean therm to find Δd. 48²+5.9²= c²

c= 48.36

Used equation to find time

Δd = V_fΔt-0.5(a)Δt²
48.36= -0.5(-9.8)Δt²
48.36 = 4.9Δt²
48.36/4.9=Δt²
9.86 =Δt²
+ - 3.14 = Δt

s=d/t
s=48.36/3.14
s=15.4 m/s

I think I was suppose to do something with 15 degrees.

 

[azizlwl]

1. Why v_f=0?
2. The vertical height difference 5.9m below the launching point.

 

[airking95]

1. Why v_f=0?
2. The vertical height difference 5.9m below the launching point.

How do I solve it without putting Vf as 0, and yes the vertical height difference is 5.9m below the launching point.

 

[azizlwl]

Have you learned about vectors?
[itex]\vec {A}=\vec {B}+\vec {C}[/itex]

The motorcyle launches at 15° above the ground.
Since it is vector in 15° direction, you can resolved it to 2 components.
Y direction which affected by gravity and a constant X direction.

 

[airking95]

Have you learned about vectors?
[itex]\vec {A}=\vec {B}+\vec {C}[/itex]

The motorcyle launches at 15° above the ground.
Since it is vector in 15° direction, you can resolved it to 2 components.
Y direction which affected by gravity and a constant X direction.

Can you please show me, how you would solve this please ??

 

[azizlwl]

If you do it once in lifetime, it is useful in giving you the answer.
I'll only tell you what prequisite knowledge that you should acquire in order to solve this type of question.

If you want to do physics problems, you should know about vectors and its operations.
Secondly you should know/remember/derive(this makes you less equations to remember) SUVAT equations.

 

[vela]

This is a projectile motion problem. What can you tell us about projectile motion? What equations do you have that apply to projectile motion?

 

[azizlwl]

If you have a question why we need vector components, then you are on the way to solve the problem.
http://imageshack.us/a/img805/2684/20946647.jpg

 

[dawn_pingpong]

I'm really really sorry to hijack, but just wondering, is the answer 21.75m/s? Attempted it as practice, and just want to check the answer if I made any errors. Sorry! And Thanks!

 

[vela]

Nope. I get v₀=25.4 m/s.

 

[dawn_pingpong]

Okay thanks lots! Time to redo then... :/