a body is projected with speed 40root2 m/s downwards an angle of 45 degree from vertical if h=100 m find 1. time of flight 2. range

Asked by sohail.saba0311 | 9th Sep, 2021, 08:23: PM

Expert Answer:

As shown in above figure, an object is projected downward from a height  h = 100 m above ground level 
with velocity u 40√2 m/s so that angle of projection is 45o with vertical.
 
Projection velocity is resolved into two components,
(i) horizontal component ux = 40 m/s and (ii) vertical component  uy = 40 m/s
 
Time of flight t , i.e., time taken for the object to reach ground is determined from the following equation
 
h = uy t + [ (1/2) g t2 ]  .................... (1)
 
where g is acceleration due to gravity .
 
By substituting values in eqn.(1) , we get  the following quadratic equation
 
100 = 40 t + 4.9 t2   or   4.9 t2 + 40 t -100 = 0
 
By solving above quadratic equation, we get t = 2 s
 
Range R , i.e. Horizontal distance from projection point is determined by following equation
 
R = ux t
 
where t is time of flight
 
Hence, we get , R = 40 × 2  = 80 m

Answered by Thiyagarajan K | 9th Sep, 2021, 09:59: PM