Kinematics- Child running down a hill

[panozg]

Homework Statement

A child runs down a 13 hill and then suddenly jumps upward at a 17 angle above horizontal and lands 1.5 down the hill as measured along the hill. What was the child's initial speed?

Homework Equations

Unknown. Been trying to use trig to solve distances and as a result velocity.

The Attempt at a Solution

distance below starting point: y=1.5sin13=0.337 m
distance away (x): x=1.5cos13=1.46 m

as a result used 1.46 to figure out height above starting position with angle 17 degrees.

1.46tan17=0.446 m

V^2-Vo^2=2ad
0-Vo^2=2(-9.8)(.446)
Vo=2.9566 m/s

sin17=2.9566/V

V=10.1 m/s

THIS IS INCORRECT

 

[willem2]

https://www.physicsforums.com/showthread.php?t=339864"

 

[tomcue]

I would first commend the student for their efforts in using trigonometry to solve the problem. However, it seems that there may be some errors in their calculations. To accurately solve this problem, we would need to consider the initial velocity of the child, the acceleration due to gravity, and the displacement of the child along the hill. Additionally, the angle at which the child jumps may also affect their final landing position.

To solve this problem, we can use the kinematic equations:

1. Displacement: x = x0 + v0t + 1/2at^2
2. Velocity: v = v0 + at
3. Final velocity: v^2 = v0^2 + 2ax

Using the given information, we can set up the equations as follows:

1. For the child's motion down the hill:
x = 0 + v0t + 1/2(9.8)t^2
2. For the child's motion up the hill:
x = 1.5 + v0t + 1/2(-9.8)t^2

Since the child lands 1.5m down the hill, we can set these two equations equal to each other and solve for t:

0 + v0t + 1/2(9.8)t^2 = 1.5 + v0t + 1/2(-9.8)t^2
1.5 = 2v0t

Now, we can use the third kinematic equation to solve for the initial velocity:

v^2 = v0^2 + 2ax
0 = v0^2 + 2(9.8)(1.5)
v0 = 4.39 m/s

Therefore, the child's initial speed down the hill was 4.39 m/s. It is important to note that this solution assumes that the child's motion is in one dimension and that air resistance is negligible.