Question

An airplane with a speed of 52.6 m/s is climbing upward at an angle of 52° with respect to the horizontal. When the plane's altitude is 760 m, the pilot releases a package.

(a) Calculate the distance along the ground, measured from a point directly beneath the point of release, to where the package hits the earth.
m

(b) Relative to the ground determine the angle of the velocity vector of the package just before impact.

° clockwise from the positive x axis

A bird watcher meanders through the woods, walking 0.30 km due east, 0.70 km due south, and 2.10 km in a direction 38.0° north of west. The time required for this trip is 2.00 h.

(a) Determine the magnitude and direction (relative to due west) of the bird watcher's displacement. Use kilometers and hours for distance and time, respectively.

magnitude	km
direction	° north of west

(b) Determine the magnitude and direction (relative to due west) of the bird watcher's average velocity.

magnitude	km/hr
direction	° north of west

Answer 1

A)

when the box is dropped, it will have the same initial velocity as that of the aeroplane.

The velocity in x-direction remains unchanged during the fall, as there is no force acting on it.

However there is the gravitational force in the -ve y-direction, hence the acceleration in the y-direction is -g.

The x and y components of the velocities are

Applying the equation of motion for the y-axis

upwards is taken as positive

Hence

putting these values

solving this quadratic equation

Taking only the positive value for t

in this interval the distance travelled on the x-axis will be

b)

using the equation of motion with the time obtained from the previous analysis, we can find out the final velocity is the y-direction (NOTE: the velocity in the x-direction remains unchanged.)............

...................................equation (2)

putting these values in equation 2

_______________________________________________________________________________________

a)

Assinging +x for east and +y for north direction.

We will decompose all the displacements in i and j and add the component-wise.

Adding all x and y components separately

final displacement

Hence the magnitude and direction of the displacement are

0.695 km, and 59.7^{o north of west.}

The direction of the average velocity is the same as the direction of the net displacement, that is 59.7 deg. North of the west.

the magnitude of the average velocity is