Projectile Motion for Range Formula:
Range: R = V02sin2θ / g
Initial velocity: V0 = square root of(Rg/sin2θ)
Acceleration of Gravity: g = V02sin2θ / R
Angle(θ) = 1/2*(arc sine(Rg/V02 ))
Where,
R = Range,
V0 = Initial velocity,
g = Acceleration of Gravity.
Step 2 :
State the equation you plan to use and plug in the values.
A ship fires its guns with a speed of 78 m/s at an angle of 12° hits the target. Calculate the range from ship to target?
Step 1 :Given that:
Initial velocity(V0) = 78m/s
angle(θ) = 12°
Range(R) = ?
Step 2 :Substitue the given values in the formula:
Range: R = V02sin2θ / g
R = (78)2sin2(12) / 9.8 [ since g = 9.8m/s2]
R = 252.509m
Answer :R = 252.509m
What angle of elevation (projection angle) should a port cannon have in order to hit a pirate ship 800m off shore. Assume the muzzle velocity of the cannon ball is 150. m/s.
Step 1 :Given that:
Initial velocity(V0) = 150m/s
Range(R) = 800m
angle(θ) = ?
Step 2 :Substitue the given values in the formula:
Angle(θ) = 1/2*(arc sine(Rg/V02 ))
θ = 1/2*(arc sine(800×9.8/(150)2 ))[ since g = 9.8m/s2]
θ = 10.196
Answer :θ = 10.196 degree
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