- #1
pdxbird
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Hi! I'm pretty sure I got the first four parts right, but I'm lost on the last one.
1. Homework Statement :
An arrow is shot from an elevation of 100 meters at a 30-degree angle. It leaves the bow with a speed of 50 meters/second.
1) Find the initial vertical component of velocity.
2) Find the vertical position function of the arrow - s(t)
3) How high will the arrow get?
4) If the ground is flat, how long will it take for the arrow to hit the ground?
5) Supposing that horizontal velocity is constant, how far from the shooting point will the arrow be when it hits the ground?
Gravity = 9.8 m/s
a(t) = v'(t)
v(t) = s'(t)
s = f(t)
1)
sin(30) = x/50
.5 = x/50
x = 25 meters/second
2)
v(t)= -9.8t + 50
s(t)= -4.9t^2 + 50t + 100
3)
Max height when v = 0
v(t)= -9.8t + 50
t = 5.13 seconds
(5.13) (50 m/s) = 256 m high
sin(30) = x/256 m
x = 128m + 100m (<-- initial vertical displacement) = 228 m high
4)
s(t)= -4.9t^2 + 50t + 100
Solving for t, the positive constant is is 11.92
So, it hits the ground after 11.92 seconds.
5)
I don't know! Help! :)
1. Homework Statement :
An arrow is shot from an elevation of 100 meters at a 30-degree angle. It leaves the bow with a speed of 50 meters/second.
1) Find the initial vertical component of velocity.
2) Find the vertical position function of the arrow - s(t)
3) How high will the arrow get?
4) If the ground is flat, how long will it take for the arrow to hit the ground?
5) Supposing that horizontal velocity is constant, how far from the shooting point will the arrow be when it hits the ground?
Homework Equations
Gravity = 9.8 m/s
a(t) = v'(t)
v(t) = s'(t)
s = f(t)
The Attempt at a Solution
1)
sin(30) = x/50
.5 = x/50
x = 25 meters/second
2)
v(t)= -9.8t + 50
s(t)= -4.9t^2 + 50t + 100
3)
Max height when v = 0
v(t)= -9.8t + 50
t = 5.13 seconds
(5.13) (50 m/s) = 256 m high
sin(30) = x/256 m
x = 128m + 100m (<-- initial vertical displacement) = 228 m high
4)
s(t)= -4.9t^2 + 50t + 100
Solving for t, the positive constant is is 11.92
So, it hits the ground after 11.92 seconds.
5)
I don't know! Help! :)