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 45^{o} with vertical.
Projection velocity is resolved into two components,
(i) horizontal component u_{x} = 40 m/s and (ii) vertical component u_{y} = 40 m/s
Time of flight t , i.e., time taken for the object to reach ground is determined from the following equation
h = u_{y} t + [ (1/2) g t^{2} ] .................... (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 t^{2} or 4.9 t^{2} + 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 = u_{x} t

where t is time of flight
Hence, we get , R = 40 × 2 = 80 m

^{o}with vertical.

_{x}= 40 m/s and (ii) vertical component u

_{y}= 40 m/s

_{y}t + [ (1/2) g t

^{2}] .................... (1)

^{2}or 4.9 t

^{2}+ 40 t -100 = 0

_{x}t

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

## Concept Videos

- Angular Displacement of a body is given by thete= 2t2+5t+3. Find angular velocity and angular acceleration
- what is RPM.is it a unit of frequency or angular velocity. If a particle complete 1 revolution in 1 sec find both sec
- The position of a particle at any instant is given by .
At what instant the velocity vector will make an angle 45
^{o}with X-axis. - A particle starts from the origin at t = 0 with a velocity of m/s and moves in XY plane with a constant acceleration of . (a) At what time is the X-coordinate of the particle 16 m? (b) What is the Y-coordinate of the particle at that time?
- A cyclist starts from the center O of circle of park of radius 1 km, reaches the edge P of the park, then cycles along the circumference to point Q and returns to the centre along QO as shown. If the round trip takes 10 minutes, then what is (a) net displacement (b) average velocity (c) average speed of the cyclist?
- The position vector of particle at any instant is given by . Show that velocity and acceleration of particle at any instant are perpendicular to each other.
- An aircraft is flying at a height of 3400m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10 s apart in 30
^{o}, what is the speed of the aircraft? - A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest taxidriver takes him along a circuitous path 23 km long and reaches the hotel in 28 minute. What is: (a) the average speed of taxi (b) the magnitude of average velocity. Are the two equal?
- Two particles A and B start from P and move along a circular path in anticlockwise and clockwise direction respectively. They complete one fourth of the journey in the same time. Do they have same average velocities?

### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change