Question

A helicopter with mass 2.35×10⁴kg has a position given by →r(t)=(0.020t3)ˆi+(2.2t)ˆj−(0.060t2)ˆk. Find the net force on the helicopter at t=3.0s.

a) 0.141 N
b)2.235 N
c) 4.670 N
d) 6.905 N

Answer 1

To find the net force on the helicopter at t=3.0s, differentiate the position vector with respect to time to get the velocity vector, then differentiate the velocity vector with respect to time to get the acceleration vector. Finally, use Newton's second law to find the net force.

Step-by-step explanation:

To find the net force on the helicopter at t=3.0s, we need to differentiate the position vector, →r(t), with respect to time to get the velocity vector, →v(t). Then, we differentiate →v(t) with respect to time again to get the acceleration vector, →a(t). Finally, we can use Newton's second law, F = m⋅a, to find the net force.

Here's how we can calculate it:

1. Differentiate →r(t) with respect to time to get →v(t).

2. Differentiate →v(t) with respect to time to get →a(t).

3. Plug in t=3.0s into →a(t) to find →a(3.0s).

4. Use Newton's second law, F = m⋅a, and plug in m and →a(3.0s) to find the net force.