a body is projected horizontally with a velocity of 80m/s from the top of a tower 160m above the ground. find the time of flight,range,velocity at which the body strikes the ground

time of flight (time to fall):

hf=hi+vi*t-1/2 9.8 t^2. In the vertical, vi is zero, hi=160, hf=0 solve for t.

range=vi*timeofflight

finalvelocity:
vertical: vf=g*timeofflight downward
horizontal=80m/s

Vfinal=vf downward + vh (parallel to ground) this is a vector equation

The speed of projection is 40m/s upward.The negative value gives the speed at which the dody again arrives at the level of projection

U2 Sin 2a

=g
=34.66m

To find the time of flight, range, and velocity at which the body strikes the ground, we can use the equations of motion. Let's break it down step by step:

1. Time of flight:
When the body is launched horizontally, we can assume that there is no initial vertical velocity (since it is only projected horizontally). The only force acting on the body is its weight (due to gravity) in the downward direction. Therefore, the time of flight can be calculated using the equation:

time = sqrt(2 * height / g)

where height is the initial vertical displacement (in this case, the height of the tower) and g is the acceleration due to gravity (typically taken as 9.8 m/s^2).

Plugging in the values:
height = 160 m
g = 9.8 m/s^2

time = sqrt(2 * 160 / 9.8)
= sqrt(320 / 9.8)
≈ sqrt(32.65)
≈ 5.71 seconds (rounded to two decimal places)

So, the time of flight is approximately 5.71 seconds.

2. Range:
The range is the horizontal distance covered by the body during its flight. Since the body is projected horizontally, the horizontal velocity remains constant throughout the motion. The range can be calculated using the equation:

range = horizontal velocity * time of flight

In this case, the horizontal velocity is given as 80 m/s (horizontally projected).

Plugging in the values:
horizontal velocity = 80 m/s
time of flight = 5.71 seconds

range = 80 * 5.71
≈ 457.6 meters (rounded to one decimal place)

So, the range is approximately 457.6 meters.

3. Velocity at which the body strikes the ground:
Since the body is only projected horizontally, the vertical velocity component remains zero throughout the motion. Therefore, the velocity at which the body strikes the ground is the same as the horizontal velocity.

Therefore, the velocity at which the body strikes the ground is 80 m/s.

To summarize:
- Time of flight: Approximately 5.71 seconds
- Range: Approximately 457.6 meters
- Velocity at which the body strikes the ground: 80 m/s