Question

3. An object of mass $m$ is launched upward with initial velocity $V$. The air resistance force is proportional to the square of the velocity. Let $h(t)$ be the height of the object which satisfies the initial value problem $mh''(t) = -mg - a[h'(t)]^2$, $h(0) = 0$, $h'(0) = V$. (a) Find the dimensions of the constant $a$. (b) Use dimensional analysis to find a formula for the height $h$ of the ball in terms of $t$ and all the parameters in the problem. Identify all the dimensionless quantities. You need to define one dimensionless time $\tau$ and dimensionless height $y$ - the class notes might be useful.

          3. An object of mass $m$ is launched upward with initial velocity $V$. The air resistance force is proportional to the square of the velocity. Let $h(t)$ be the height of the object which satisfies the initial value problem
$mh''(t) = -mg - a[h'(t)]^2$, $h(0) = 0$, $h'(0) = V$.
(a) Find the dimensions of the constant $a$.
(b) Use dimensional analysis to find a formula for the height $h$ of the ball in terms of $t$ and all the parameters in the problem. Identify all the dimensionless quantities. You need to define one dimensionless time $\tau$ and dimensionless height $y$ - the class notes might be useful.

3. An object of mass m is launched upward with initial velocity V. The air resistance force is proportional to the square of the velocity. Let h(t) be the height of the object which satisfies the initial value problem
mh”(t) = -mg - a[h'(t)]^2, h(0) = 0, h'(0) = V.
(a) Find the dimensions of the constant a.
(b) Use dimensional analysis to find a formula for the height h of the ball in terms of t and all the parameters in the problem. Identify all the dimensionless quantities. You need to define one dimensionless time τ and dimensionless height y - the class notes might be useful.

Added by Josep S.

Question

Please give Ace some feedback