Part B Please In the absence of air resistance, a projectile that lands at the e
ID: 1491932 • Letter: P
Question
Part B Please
In the absence of air resistance, a projectile that lands at the elevation from which it was launched achieves maximum range when launched at a 45 degree angle. Suppose a projectile of mass m is launched with speed v_0 into a headwind that exerts a constant, horizontal retarding force F vector_wind = F_wind i cap. Find an expression for the angle at which the range is maximum. By what percentage is the maximum range of a 0.700 kg ball reduced if F_wind = 0.900 N ? Express your answer with the appropriate units.Explanation / Answer
B) In the absence of air resistance,
• range x = V²sin(2) / g, so for = 45º
x = V² / g
• flight time t = 2·V·sin/g, so for = 45º
t = 2*V*2/2 / g = (V/g)*2
The acceleration in the x-direction due to the wind is
a = F / m = 0.900N / 0.700kg = 1.286 m/s²
so the reduction in range is
s = ½at² = ½ * 1.286m/s² * [(V/g)*2]² = 1.286m/s² * V² / g²
and finally
s / x = (1.286m/s²*V² / g²) / (V²/g) = 1.286m/s² / g
s / x = 1.286 / 9.8 = 0.131 = 13.1%
Hope this helps!