Question

An object follows functions at y= 3x³ (m/s) and z= 5x⁰.⁵ (m/s).

With a horizontal velocity of 1.6t (m/s), what is the magnitude of
its velocity at t= 0.7s?

Answer 1

To find the magnitude of the velocity at t=0.7s, you need to find the derivatives of the given functions and substitute t=0.7s into the derivatives to find the magnitude of the velocity in the y-axis and z-axis. The magnitude of the velocity at t=0.7s is √(4.83²+6.87²)=8.61 m/s.

Step-by-step explanation:

To find the magnitude of the velocity at t=0.7s, we need to find the derivatives of the given functions. The derivative of y=3x³ with respect to x is dy/dx=9x², and the derivative of z=5x⁰.⁵ with respect to x is dz/dx=(2.5/x⁰.⁵).

We can then substitute t=0.7s into the derivative of y to find the magnitude of the velocity in the y-axis, and substitute t=0.7s into the derivative of z to find the magnitude of the velocity in the z-axis.

Substituting t=0.7s into dy/dx=9x², we get dy/dt=9(0.7)²=4.83 m/s. Substituting t=0.7s into dz/dx=2.5/(x⁰.⁵), we get dz/dt=2.5/(0.7⁰.⁵)=6.87 m/s. Therefore, the magnitude of the velocity at t=0.7s is √(4.83²+6.87²)=8.61 m/s.