Question

A sling is used to give a stone an initial velocity of 20 at an angle of 30 above the horizontal. The stone travels through the air and lands a horizontal distance of 32m from where it was released. If the stone returns to the same height from which it was thrown, which of the following claims best describes the motion of the air through the stone's trajectory? There must be a horizontal wind in the direction of the stone's motion, because ignoring air resistance when alculating the horizontal range would yield a value less than 32m There must be a horizontal wind opposite the direction of the stone's motion, because ignoring air resistance when calculating the horizontal range would yield a value less than 32m. (C) There is no horizontal wind, because ignoring air resistance when calculating the horizontal range would yield a value equal to 32m. There must be a horizontal wind in the direction of the stone's motion, because ignoring air resistance when calculating the horizontal range would yield a value greater than 32m. There must be a horizontal wind opposite the direction of the stone's motion, because ignoring air resistance when calculating the horizontal range would yield a value greater than 32m

Answer 1

Option E is correct.

There must be a horizontal wind opposite the direction of the stone's motion, because ignoring air resistance when calculating the horizontal range would yield a value greater than 32 m.

Step-by-step explanation:

Normally, ignoring air resistance, for projectile motion, the range (horizontal distance teavelled) of the motion is given as

R = (u² sin 2θ)/g

where

u = initial velocity of the projectile = 20 m/s

θ = angle above the horizontal at which the projectile was launched = 30°

g = acceleration due to gravity = 9.8 m/s²

R = (30² sin 60°) ÷ 9.8

R = 78.53 m

So, Normally, the stone should travel a horizontal distance of 78.53 m. So, travelling a horizontal distance of 32 m (less than half of what the range should be without air resistance) means that, the motion of the stone was impeded, hence, option E is correct.

There must be a horizontal wind opposite the direction of the stone's motion, because ignoring air resistance when calculating the horizontal range would yield a value greater than 32 m.

Hope this Helps!!!