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quicksilver123
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Homework Statement
A child sitting in a tree throws his apple core from where he is perched (a height of 4.0m) with a velocity of 5.0m/s [35 deg above horizontal] and it hits the ground right next to his friend.
a)how long is it before the apple core hits the ground?
b)how far from the base of the tree will the apple core land?
c)what is the velocity of the apple core on impact?
Homework Equations
suvat
pythag.
quad. form.
The Attempt at a Solution
Given:
Vi=5.0m/s [35 deg above horizontal]
Δdy = 4.0m
a)
Find Δt.
Let [down] and [forward] be positive.
Initial Velocity Components:
Vix = 5m/s (cos35) = 4.095760221m/s
Viy = 5m/s (sin35) = -2.867882182m/s
*Note: I threw the negative on the y-component because it is traveling upwards.
Acceleration Components:
ax = 0m/s/s
ay = 9.8m/s/s
Calculation for part A:
Δdy = ViyΔt +1/2 (ay)Δt2
4.0m = -2.867882182m/s Δt + 4.9m/s/s (Δt2)
In order to isolate the time variable, I rearranged to the form ax2+bx+c=0 and solved via the quadratic formula.
The only real root yielded was x=1.242359580605109
Therefore, Δt = 1.242359580605109 seconds
b)
Find Δdx.
Calculation for part B:
Δdx = VixΔt +1/2 (ax)Δt2
Δdx = 4.095760221m/s (1.242359580605109 seconds) + 0
Δdx = 5.08840695042 m
c)
Find Vf
Components of Vf:
Vfx
Vfx2 = Vix2+2axΔdx
Since ax=0m/s/s, Vfx=Vix
∴ Vfx=5m/s
Vfy
Vfy2 = Viy2+2ayΔdy
Vfy2 = 8.22474821m2/s2 + 78.4m2/s2
Vfy = √86.62474821
Vfy = 9.307241708m/s
Vf = √(Vfx2 +Vfy2
Vf = √14.30724171
Vf = 3.782491469m/s
Answers rounded:
Δt = 1.24 seconds
Δdx = 5.088 m
Vf = 3.78 m/s
I know the sig digits aren't correct but I didn't want to sacrifice accuracy.
Are these answers correct?
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