Question

A projectile is fired horizontally with a velocity of 50 m/s from top of a hill 500 m high.(take g=10m/s^2) calculate: 1. time taken for it to reach the ground. 2. the horizontal range.

Answer 1

The time taken by the projectile to reach the ground is 10sec.

The horizontal range is 500m.

• Initital velocity = 50m/s , in horizontal direction
• Initial height =  500m
• g= 10m/s^2
• By equations of motion, s =ut + 0.5at^2, s = distance,a = acceleration
• u = initial velocity in vertical direction  = 0m/s

• by equation, s = 0.5at^2 ==> t = $\sqrt{\frac{2s}{a} } = \sqrt{\frac{2h}{g} }$

• t = $\sqrt{\frac{1000}{10} } = \sqrt{\frac{100}{1} } =10s$

To find the horizontal range,

• Here acceleration in horizontal direction = 0.

• Using same equation as before, R =Vt + 0.5at^2
• Range =  Vxt, V = velocity in horizontal direction, a constant since a =0
• Range = 50m/s x 10s = 500m

Answer 2

Time taken for it to reach the ground = 6.18 sec.

Horizontal range =  309 meter.

Given:

A projectile is fired horizontally with a velocity of 50 m/s from top of a hill 500 m  high.

Acceleration due to gravity: 10m/s²

To find:

1. Time taken for it to reach the ground.

2. The horizontal range.

Formula used:

        S=ut+  $\frac{1}{2}$ gt²

Horizontal range = ut

Where,     S = distance traveled

                 u= initial velocity

                 g=  Acceleration due to gravity

                 t = Time of flight

Explanation:

A projectile is fired horizontally from height  so this motion is along the gravity hence Acceleration due to gravity is positive.

Height = S = 500 m

u= initial velocity = 50 m/s

         S=ut+  $\frac{1}{2}$ gt²

    500= 50×t +  $\frac{1}{2}$ 10×t²

    500= 50×t +  5×t²

      t= 6.18 sec.

Horizontal range = ut

                            = 50× 6.18

                            = 309 meter

Time taken for it to reach the ground = 6.18 sec.

Horizontal range =  309 meter.

To learn more....

1)The equation of the path of the projectile is y=0.5x-0.04x^2.the initial speed of projectile is.

https://brainly.in/question/4372517

2)A projectile is fired at a speed of hundred metre per second at an angle of 37 degrees above the horizontal .At the highest point the projectile breaks into two parts of mass ratio 1:3 the smaller coming to rest .find the distance from the launching point where the heavier piece lands.

https://brainly.in/question/13668979