A person driving through a field has velocity components that are 30 m/s west an

Question

A person driving through a field has velocity components that are 30 m/s west and 20 m/s south. What is the approximate direction of the overall velocity? 48° 214 34° 34 13 of 20 A student kicks a ball that is initially at rest on the ground. The ball leaves the student's foot with some velocity v at an angle e. When the ball is at its maximum height, which statement is most accurate? At the maximum height, the velocity of the ball is zero At the maximum height, the acceleration of the ball is zero. Both of the above are true None of the above are true. 14 of 20 Suppose that an airplane flying 70 m/s at a height of 300 m drops a crate. What horizontal distance will the crate have traveled when it hits the ground? Assume negligible air resistance. 21000 m 548 m 242 m 61 m

Explanation / Answer

First Question –

Write the velocity in ‘i’ and ‘j’ components

V = 30(-i) + 20(-j)

So, ? = tan^-1(-20 / -30) = 33.7 deg = 34 deg.

Here, both x and y components are negative.

So, the direction of the overall velocity from the positive direction of x – axis = 180+34 = 214 deg.

Hence second option is the correct answer.

13 of 20:

At the maximum height, only vertical component of the velocity Vy = 0

The ball will have horizontal component of velocity, Vx, and this will remain constant.

So, neither of the two statements is correct.

Hence, last option is the correct answer.

14 of 20:

First determine the time taken by the crate to cover a vertical distance of h = 300 m.

use the expression –

h = u*t + (1/2)*g*t^2

=> 300 = 0 + 0.5*9.8*t^2

=> t^2 = 300 / 4.9

=> t = 7.82 s

Horizontal distance covered by the crate in this time = Vx * t = 70 * 7.82 = 547.4 m

Hence second option is the correct answer.

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