(a) A small projectile is launched from the ground and lands on the ground at the...

(a) A small projectile is launched from the ground and lands on the ground at the same height. Assuming linear air resistance, compute the time that the projectile travels under the following conditions: launch speed v0 = 4.00 m/s launch angle θ = 30.0 degrees retarding constant k = 1.00 1/s You may use the perturbation method (b) Compute the horizontal distance that the projectile travels.

Solutions

Expert Solution

The equation of motion of the projectile motion is

K= positive constant . define

be the terminal velocity. In the component form the above equation can be written as

integrating the equation for x component of velocity

.This expression clearly tells as that air drag causes the projectiles horizontal velocity to decay exponentially . Integrating once again we get

and when

Similarly integrating the y equation twice we will get

and the time of flight can be obtained as by setting y=0.And for

v_t=9.790m/s

genius_generous answered 1 year ago

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