Finding speed of the car, kinematics

[jehan4141]

This is an even numbered problem from Cutnell and Johnson 8 edition...Can somebody tell me if the answer is correct? I spent a good 30 minutes dissecting the problem, so here's to hoping I am right :)

A child operating a radio-controlled model car on a dock accidentally steers it off the edge. The car's displacement 1.1 s after leaving the dock has a magnitude of 7.0 m. What is the car's speed at the instant it drives off the edge of the dock?

Given
t = 1.1 s
V_oy = 0 m/s
The displacement after 1.1 seconds is 7 meters. This means, from the point where it fell off the edge of the dock, to its position after 1.1 seconds, the distance between the two points is 7 meters.

We are trying to find V_ox which is the same thing as V_x because there's no acceleration in the x-direction.

My Work
V_oy = 0 m/s

Find V_y when t = 1.1 seconds passes

V_y = V_oy + at = 0 - (-9.8*1.1)
V_y = -10.78 m/s

Find the distance it has fallen in the y-direction during the 1.1 seconds.
y = V_oyt + 0.5at² = 0.5(-9.8)(1.1²)
y = -5.929 meters

Using A² + B² = C²
5.929² + B² = 7²
B = 3.72114 meters <----this is the distance in the x direction that it travels during 1.1 seconds

So Vx = B/t = 3.72114/1.1
Vx = 3.383 m/s

PRETTY PLEASE LET THIS BE CORRECT *fingers crossed*

 

[ehild]

Hi, Jehan,

your work is correct and nice, but why have you calculated vy? It was not needed.

ehild

 

[danielakkerma]

Hi!
It seems like the reasoning and execution is flawless, good job!
One point though, just for future reference: there's a lot to be said for rounding off, on occasion.
You have your v_y there, at 5.92... It's not unreasonable to bring to ~6...
Daniel

 

[jehan4141]

thank you both! it feels so stressful not knowing whether it is right or wrong. having both your approval puts me at ease! i can finally get some sleep! thank you!