Question

1. A carpenter tosses a shingle horizontally off an8.82-m-high roof,and it hits the ground a horizontal distance of 15.0 m away.

A. How long was the shingle in the air?
B. How fast was it thrown?

A railroad locomotive can exert a 350-kN force. By itself, it accelerates at 1.2 m/s2; when pulling a train, the acceleration drops to 0.088 m/s2.

A. Find the mass of the locomotive.
B. Find the mass of the remainder of the train.

Answer 1

1) maximum height = H = 8.82 m

horizontal distance =15 m

A) TO CALCULATE THE TIME IT SPENDS IN AIR :

Time of flight= time of ascent + time of descent

T = u /g + u/g

T = 2u /g

where u is the initial velocity and g is acceleration due to gravity

firstly we have to calculate u from the given maximum height

   H = u² /2g

sqrt ( 8.82 * 2 * 10 )= u

u = 13.282 m / sec

T= 2 u/g

T= 2 * 13.282 /10 =2.656 sec

B) V² = 2gh

=2 * 10 * 15

v=17.320 m/sec

part ii:

(a)force exerted by the locomotive = F = mass * acceleration

F = ma ------------------(1)

acceleration = 1.2 m/sec^{2 ----------------(2)}

force = 350 KN   

= 350 * 10³ N ---------------------(3)

substituting 2 and 3 in equation (1) we get,

350 * 10³ = mass * 1.2

350 * 1000 / 1.2 = mass of the locomotive

therefore mass of the locomotive = 291666.6667 kg

= 291666.67 kg

(B) Force exerted by the locomotive = F

now the mass=M= mass of the train remainder + mass of locomotive

let the mass of the train remainder= m1 = ?

the mass of the locomotive = m2 = 291666.67kg

acceleration a= 0.088 m/sec²

from Newtons laws we have,

F =ma

F = (m1 + m2) * a

350 * 1000 = (m1 + 291666.67 ) * 0.088

350 * 1000 / 0.088 = m1 + 291666.67

m1 = 3685606.057 kg

  therefore the mass of the remainder of the train = 3685606.057kg