It is apocalyptic future, and zombies are trying to take over the world. In an e

ID: 1656050 • Letter: I

Question

It is apocalyptic future, and zombies are trying to take over the world. In an effort to save

the people, our hero aims his bow at a

zombie that is slowly approacing them.

The zombie is walking towards them at 1.25 m/s.

He fires the arrow at 20

above the horizon,

hits the zombie, and saves the day.

Given that the bow will fire an arrow at a

speed of 90.0 m/s, and assuming that the

arrow beging and ends at the same height,

how far away is the zombie (distance d)

when our hero fires the shot?

Find the direction and magnitude of the arrow's velocity relative to the zombie just before

u = 90 m/s @ 20degrees

Let the horizontal distance be sx

Hence,

ux = 90cos(20)
uy = 90sin(20)

Now,
Let time taken to reach the maximum height be t
At maximum height the veritcal velocity will be 0

Hence
0 = 90sin(20) - 9.8*t
t = (90sin(20))/9.8
t = 3.14

Total time = 2*t = 6.28 secs

Now the horizontal distance travelled = 6.28*90cos(20) = 531.114 m

A)
How far was the zombie :
Zombie would have also travelled a distance of = 6.28*1.25 = 7.85 m

Distance of zombie = distance travelled by zombie + Distance travelled by arrow
Distance of zombie = 7.85 + 531.114
Distance of zombie = 538.964 m

B)
Velocity of zombie = -1.25 i + 0 j
Velocity of arrow = 90cos(20)i - 90sin(20)j = 83.33 i - 30.78 j

Magnitude = ((83.33)^2 + (-30.78)^2)^(1/2) = 88.83 m/s

Angle = Arctan(-30.78/83.33) = -20.27 degrees

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.