Question

Katniss Everdeen can shoot an arrow at an impressive 95 m/s How high above the initial height would an arrow go if it was shot straight upwards at this speed?

How long is the arrow in the air before it hits the ground, if it was shot from an initial height of 1.5 m?

Answer 1

1)

vi = 95 m/s

vf = 0 m/s (at maximum height, speed is 0)

a = -9.8 m/s^2

use:

vf^2 = vi^2 + 2*a*d

0 = 95^2 + 2*(-9.8)*d

19.6*d = 9025

d = 460 m

Answer: 460 m

2)

Displacement when arrow hit ground,

d = -1.5 m

a = -9.8 m/s^2

v= 95 m/s

use:

d = vi*t + 0.5*a*t^2

-1.5 = 95*t - 0.5*9.8*t^2

4.9*t^2 - 95t - 1.5 = 0

Let's solve this quadratic equation

Comparing it with general form: (at^2+bt+c=0)

a = 4.9

b = -95

c = -1.5

solution of quadratic equation is found by below formula

t = {-b + √(b^2-4*a*c)}/2a

t = {-b - √(b^2-4*a*c)}/2a

b^2-4*a*c = 9.054*10^3

putting value of d, solution can be written as:

t = {95 + √(9.054*10^3)}/9.8

t = {95 - √(9.054*10^3)}/9.8

solutions are :

t = 19.4 and t = -1.578*10^-2

since t can't be negative, the possible value of t is

t = 19.4

Answer: 19.4 s