The equation Bold r (t )equals(StartFraction StartRoot 3 EndRoot Over 3 EndFraction t )Bold i plus (t minus 16 t squared )Bold j is the position of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t equals 0.

150°

Explanation:

Given the position of a particle in space at a time t expressed as;

Velocity of the body at t = 0 will be expressed as shown;

To get the angle between the velocity and acceleration at t = 0, we will use the formula for calculating the dot product of two vectors.

Substituting the values given into the formula, we will have;

Since cos is negative in the second quadrant, the angle between the velocity and acceleration will be 180 - 30 = 150°

Distance covered, s = 8ft - 4ft = 4 ftinitial velocity, u = 34 ft/sthe acrobat is moving upwards and therefore, a = -g = -9.81 m/s^2 = 32.19 ft/s^2applying equation of motion; s = ut -1/2gt^2then,4 = 34t -1/2*32.19t^24 = 34t - 16.095t^2rearranging; -16.095t^2 + 34t - 4 = 0solving the quadratic equation; t = {-34 +/- sqrt [34^2 - 4(-16.)]}/2(-16.095) = 1.06 +/- 0.93 = 0.13 or 1.99the acrobat will take 0.13 seconds to be at 8 ft above the ground. additionally, once at the maximum height, the acrobat will move down and be at the same spot (that is height) after 1.99 seconds moving down.

B. conditioned response