Question

A sand bag is dropped from a balloon at a height of 60 meter when the angle of elevation to the sun is 300. The position of the sandbag is s(t)= 60-4.9t². Find the rate at which the shadow of the sand bag is travelling along the ground when the sand bad is at a height of 35 meters.

Answer 1

The rate at which the shadow of the sandbag is traveling along the ground is -343 m/s.

Step-by-step explanation:

To find the rate at which the shadow of the sandbag is traveling along the ground, we need to find the derivative of the position function with respect to time. The position function is given as s(t) = 60 - 4.9t², where s represents the height of the sandbag and t represents time. The derivative of s(t) with respect to t can be found using the power rule of differentiation. Taking the derivative, we get:

s'(t) = -9.8t

When the sandbag is at a height of 35 meters, we can substitute this value into the derivative to find the rate at which the shadow is traveling along the ground:

s'(t) = -9.8t

s'(t) = -9.8 * t

s'(t) = -9.8 * (35)

s'(t) = -343 m/s

Therefore, the rate at which the shadow of the sandbag is traveling along the ground when the sandbag is at a height of 35 meters is -343 m/s.