A projectile is fired uphill as sketched in Figure P4.90. If v0 = 173 m/s and θ = 30°, find L.
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To find the value of L, which is the range of the projectile, we can use the equation for horizontal range:
L = (v0^2 * sin(2θ)) / g
where:
- L is the range of the projectile
- v0 is the initial velocity of the projectile
- θ is the angle of projection
- g is the acceleration due to gravity
Let's plug in the given values:
v0 = 173 m/s
θ = 30°
g ≈ 9.8 m/s² (assuming gravitational acceleration)
L = (v0^2 * sin(2θ)) / g
Now, we can calculate L.
First, let's calculate sin(2θ):
sin(2θ) = sin(2 * 30°) = sin(60°) = √3 / 2 ≈ 0.866
Now, plug in the values:
L = (173^2 * 0.866) / 9.8
Simplifying further:
L = (29929 * 0.866) / 9.8
L ≈ 2626.09 / 9.8
L ≈ 268.19 meters
Therefore, the range (L) of the projectile is approximately 268.19 meters.