Question

As preparation for this problem, review Conceptual Example 10. The drawing shows two planes each dropping an empty fuel tank. At the moment of release each plane has the same speed of 107 m/s, and each tank is at the same height of 1.12 km above the ground. Although the speeds are the same, the velocities are different at the instant of release, because one plane is flying at an angle of 15.0° above the horizontal and the other is flying at an angle of 15.0° below the horizontal. Find the (a) magnitude and (b) direction of the velocity with which the fuel tank hits the ground if it is from plane A. Find the (c) magnitude and (d) direction of the velocity with which the fuel tank hits the ground if it is from plane B. In each part, give the direction as a positive angle with respect to the horizontal.

Answer 1

a )

the distance above ground y = 1.12 km

= 1120 m

speed v = 107 m/s

= 15^o

a_y = - g = - 9.8 m/sec² ,

a_x = 0 m/sec²

V_y = v sin15

= 107 X sin15

= 27.69 m/s

V_x = v cos15

= 107 X cos15

= 103.35 m/s

V_oy²= V_y² - 2 a_y y

= 27.69² + 2 X 9.8 X 1120

V_oy = 150.727 m/s

V_ox = 103.35 m/s

V = ( V_oy² + V_ox² )^1/2

V = ( 150.727² + 103.35² )^1/2

V = 182.75 m/s

b )

= tan^-1 ( V_oy / V_ox )

= tan^-1 ( 150.727 / 103.35 )

= 55.56^o respect to horizontal

c )

V_oy²= V_y² - 2 a_y y

= 27.69² + 2 X 9.8 X 1120

V_oy = 150.727 m/s

V_ox = 103.35 m/s

V = ( V_oy² + V_ox² )^1/2

V = ( 150.727² + 103.35² )^1/2

V = 182.75 m/s

d )

= tan^-1 ( V_oy / V_ox )

= tan^-1 ( 150.727 / 103.35 )

= 55.56^o respect to horizontal