Question

1. An elephant of mass 2000 kg is walking with a kinetic energy of 53 KJ, Find the speed of the elephant?
2. Galileo drops a stone from the leaning tower of Pisa, The stone hits the ground at a speed of 35 m/s. What is the height of the tower?
3. A car is travelling at 10 m/s. When brakes are applied, it comes to rest in 8 m due to an average force of 8000 N. What is the mass of the car?

Answer 1

Answer:

Step-by-step explanation:

Fiven:

a) Mass of elephant =2000 kg

Velocity =5 m/s

Momentum =2000×5=10000 kg. m/s

b) Mass of bullet =0.02 kg

Velocity =400 m/s

Momentum =0.02×400=8 kg.m/s

2 Given,

\theta= 69 degrees

t = 5.2 sec ; r = 15m

(a) r = Vo2 sin(2\theta) / g

Vo2 = r g / sin(2\theta) = 15 x 9.8 / sin (2x69) = 147/0.669 = 219.73

Vo = sqrt(219.73) = 14.82 m/s

Hence, Vo = 14.82 m/s

(b)Let the max height reached be H

Now the y comp of velocity will be

Voy = Vo sin(\theta) = 14.82 x sin69 = 13.83 m/s

Now the time taken by the rock to reach the max height will be given by

t' = Voy / g = 13.83/9.8 = 1.41 sec

From eqn of motion we have, s = ut + 1/2gt2,

h = 1/2 g t'2 = 1/2 x 9.8 x (1.41)2 = 9.74 meters

again we are provided with t = 5.2 sec

time for the rock to fall freely from max height, t'' = 5.2 - 1.41 = 3.8 s

h '= 1/2 g t''2 = 0.5 x 9.8 x (3.8)2 = 70.8 m

Hence, the max height H = h' - h = 70.8 - 9.74 = 61.06 m

Hence, H = 61.1 meters

c)Vertical speed of the rock just before hitting the groung will be

Vy = sqrt(2 g H) = sqrt (2 x 9.8 x 61.1) = 34.6 m/s

Horizontal speed, Vox = Vo x cos(\theta) = 14.82 x cos(69) = 5.3 m/s

So the final speed of rock = sqrt [ (34.6)2 + (5.3)2] = 35 m/s

Hence, final speed = V = 35m/s