Question

A projectile is fred horizontally into a resisting medium with a velocity v0​=3.6 m/s and the resulting deceleration is equal to cv 5, where c=0.047 m−4 s−3, and v is the velocity within the medium. Find the velocity v of the projectile at time t=6.7 s after penetration.

Answer 1

To find the velocity of the projectile at time t=6.7s after penetration, use the equation v(t) = (1/5ct + C)^(-1/4), where c = 0.047 m^-4 s^-3

Step-by-step explanation:

To find the velocity of the projectile at time t=6.7s after penetration, we can use the equation for deceleration due to a resisting medium: a = -cv^5, where c = 0.047 m^-4 s^-3.

Rearranging the equation, we have dv/dt = -cv^5.

Integrating both sides, we get v^-5dv = -cdt.

Integrating again and solving for v, we get v(t) = (1/5ct + C)^(-1/4), where C is a constant of integration

Plugging in the given values, we have v(6.7) = (1/(5*0.047*6.7) + C)^(-1/4)

Since the constant C is not given, it cannot be determined from the information given in the question