# Math Help - Sandbag Shadow Problem

Okay so....
A sandbag is dropped from a balloon at a height of 60 meters when the angle of elevation to the sun is 30 degrees. Find the rate at which the shadow of the sandbag is traveling along the ground when the sandbag is at a height of 35 meters.

Position Function: s(t) = 60-4.9t^2

Help would be much appreciated...this one is giving me fits..I think I want to solve this by proportion but I'm really not sure.

Okay so....
A sandbag is dropped from a balloon at a height of 60 meters when the angle of elevation to the sun is 30 degrees. Find the rate at which the shadow of the sandbag is traveling along the ground when the sandbag is at a height of 35 meters.

Position Function: s(t) = 60-4.9t^2

Help would be much appreciated...this one is giving me fits..I think I want to solve this by proportion but I'm really not sure.
proportions is the right way to go ...

vertical path of the sandbag is the short leg of a 30-60-90 triangle.

horizontal path of the shadow is the long leg of the same 30-60-90 triangle.

the respective velocities of each will have the same relationship.

first, set $s(t) = 35$ , solve for $t$.

in the vertical direction, the sandbag will have the velocity $s'(t) = v(t) = -9.8t$ . the velocity vector in the horizontal direction (the shadow) ...

$v(t) = -9.8t \cdot \sqrt{3}$