Question

A cargo plane is flying horizontally at an
altitude of 14.7 km with a constant speed of
994 km/hr when a large crate slides out of
the rear of the plane. A conceptual sketch is
shown.
994 km/hr
14.7 km
x
How long does it take the crate to hit
the ground? The acceleration of gravity is
9.81 m/s
2
.
1. 54.7443
2. 47.3562
3. 51.0841
4. 49.4619
5. 48.8397
6. 52.2676
7. 45.3776
8. 53.9944
9. 53.425
10. 50.0764
Answer in units of s

Answer 1

Answer:

1. 54.74433 s

Explanation:

h = Height of plane = 14.7 km

$u_x$ = Velocity of crate in x direction = 994 km/h = $276.11\ \text{m/s}$

a = g = Acceleration due to gravity = $9.81\ \text{m/s}^2$

$h=u_yt+\dfrac{1}{2}at^2\\\Rightarrow t=\sqrt{\dfrac{2h}{g}}\\\Rightarrow t=\sqrt{\dfrac{2\times 14700}{9.81}}\\\Rightarrow t=54.74433\ \text{s}$

Time the crate takes to hit the ground is 54.74433 s