Question

A lorry is travelling at a constant velocity of 10m/s when the driver sees a cow 50m in front of him

on the road. He hits the brakes to stop the truck. The truck retards at a rate of 1.25ms-2

. His reaction time

to hit the brakes is 0.5 seconds. Will the lorry hit the cow?​

Answer 1

Given:

Initial velocity of lorry, u= 10 m/s

Initial distance of cow from lorry, D= 50 m

Final velocity of lorry, v= 0 m/s

(Since, driver stops the lorry)

Acceleration of truck, a= -1.25 m/s²  

(Since, acceleration is opposite to retardation in sign but have same magnitude)

Reaction time of driver, t'= 0.5 s

To Find:

Possibility that lorry will hit cow or not

Solution:

We know that,

• $\pink{\boxed{\bf{Distance=Speed\times Time}}}$

• According to third equation of motion for constant acceleration,

$\purple{\boxed{\bf{v^{2}-u^{2}=2as}}}$

where,

v is final velocity

u is initial velocity

a is acceleration

s is displacement

$\rule{190}{1}$

Let the distance travelled by lorry before the driver applied the brake be d'

So,

$\longrightarrow\rm{d'=10\times0.5}$

$\longrightarrow\rm{d'=5\:m}$

$\rule{190}{1}$

Let the distance travelled by lorry after applying brake be d

So, on applying third equation of motion on lorry, we get

$\longrightarrow\rm{v^{2}-u^{2}=2as}$

$\longrightarrow\rm{(0)^{2}-(10)^{2}=2(-1.25)d}$

$\longrightarrow\rm{-100=-2.5d}$

$\longrightarrow\rm{-2.5d=-100}$

$\longrightarrow\rm{d=\dfrac{-100}{-2.5}}$

$\longrightarrow\rm{d=40\:m}$

$\rule{190}{1}$

Now, let total distance covered by lorry after driver sees the cow be S

So,

$\longrightarrow\rm{S=40+5}$

$\longrightarrow\rm{S=45\:m}$

Now let us calculate D-S

$\longrightarrow\rm{D-S=50-45=5\:m}$  

This shows that lorry will stops 5 m before the cow.

Since, the initial distance between lorry and cow is greater than the total distance travelled by lorry after driver sees the cow.

Hence, the lorry will not hit the cow.  

Answer 2

Answer:

wowjejejebevvehsjwehheehe