Question

(2 dimensions, 1 object, 2 accelerations)

1) A projectile is thrown with a wind. The wind produces a constant acceleration of 2 m/s/s in the same direction as the projectile’s horizontal direction. The projectile is launched with a velocity of 20 m/s at an angle of 30°. The projectile lands at the same height as it was launched.

a. How far from the launch point does the projectile land? Do this problem again with no numbers.

b. Calculate the range as a function of the initial speed vi and launch angle θ and the two constant accelerations from the wind +a and from gravity –g.

c. If the values of vi, a, and g are fixed, at what angle θmax does this situation produce the maximum range?

d. Check your answer by finding R (using answer b) at θmax, at θmax +1°, and at θmax–1° for vi = 20 m/s, a = 2 m/s/s right, and g = 10 m/s/s down.

Answer 1

Summary :

Using equations of motion in both x and y direction. We can find out the relevant quantities like range, time of flight etc. But this time we also have acceleration in x direction unlike normal case where we ignore presence of air. Finally we can find out maximum range also.