Question

A boy fallen freely from a building of height 320 m after 5 second superman jumps downward with initial speed u. Such that the boy can be saved . The minimum value of u is (assume g=10m/s^2)

Answer 1

Concept:

• Free fall
• Vertical one-dimensional motion

Given:

• Height of the building = 320m
• Time elapsed before superman jumps downward = 5s
• The speed with which superman jumps downward = u
• g=10m/s^2

Find:

• The initial speed u of superman

Solution:

The distance the boy has fallen in 5 s

s= ut+1/2gt^2

Initial velocity of boy is 0, u= 0

s = 0+ 1/2 (10) 5^2

s = 125m

Suppose superman catches the boy at a distance x from the top

x = ut + 1/2g (t^2)

x = ut+5t^2

At 125m from the top, the boy has velocity u = gt = 50m/s

The distance covered by the boy from the time superman jumps is

x-125 = 50t +1/2 (10) t^2

x-125 = 50t + 5t^2

x = ut+5t^2

ut+5t^2 - 125 = 50t + 5t^2

ut -125 = 50 t

ut-50t = 125

t (u-50) = 125

u = 91.6m/s

The initial speed u of superman is 91.6m/s

#SPJ2

Answer 2

Answer:

Concept:

When an item goes along a route, its velocity determines how quickly it moves as well as the direction it is going in. It follows that velocity is both a scalar and a vector quantity. The distance an item covers in a given amount of time is referred to as its velocity. The orientation of the item is not taken into consideration. There is simply size, in other words. Thus, the velocity is referred to as a scalar number. It is rather simple to calculate speed mathematically. By dividing the whole distance travelled by the total time it takes to complete that distance, one may determine an object's average speed. Contrarily, the mathematical calculation of velocity is more difficult and may be done in a variety of methods based on the knowledge of the object's motion that is available. By dividing the change in location (r) by the change in time (t), the average velocity may be determined in its most basic form.

Given:

The height of the building = 320m

Initial Time = 5 second

To Find :

Minimum value of u = ?

Solution :

$V_{5sec}$= gt = 10 × 5

        = 50 ms-1

$V_{sec}$ = u

Relative Velocity = u-50

X= (1/2)×gt2

   = (1/2)×10×25

  = 125 m

Since the boy has already fallen down to 125 m, Superman has to reach him before     =>     325-125=195 metres

Total time it would take to fall to 320 metres = SQRT (2u/g)

             = $\sqrt{\frac{(2 \times 320}{10}}$

             = $\sqrt{64}$

             = 8 secs

Remaining Time left : 3 sec

In order to save the boy superman have to fall down to 320 metres in 3 seconds

S = ut + ½ gt2

         320 = u × 3 + ½ × 10 × (3)2

         320 = 3u + 45

           3u = 275

             u = 91.6$ms^{-1}$

#SPJ3