An object is launched horizontally from a height of 45 m above the ground with a speed of 10 m/s. The time at which the object will hit the ground is : (Take g = 10 m/s2)
3 s
To determine the time at which an object launched horizontally from a given height will hit the ground, we focus primarily on the vertical motion. Since the object is launched horizontally, its initial vertical velocity is zero.
Step-by-step Solution:
- The object is launched horizontally from a height of 45 meters.
Initial vertical velocity, \(u = 0 \, \text{m/s}\)
Gravitational acceleration, \(g = 10 \, \text{m/s}^2\)
- To find the time \((t)\) it takes for the object to hit the ground, we use the second equation of motion for vertical displacement:
\(S = ut + \frac{1}{2}gt^2\)
- where
\(S = 45 \, \text{m}\) is the vertical displacement (height of fall)
- Substitute the values into the equation:
\(45 = 0 \times t + \frac{1}{2} \times 10 \times t^2\)
- Simplifying,
\(45 = 5t^2\)
- Solve for \(t^2\):
\(t^2 = \frac{45}{5} = 9\)
- Therefore, \(t = \sqrt{9} = 3 \, \text{s}\)
Thus, the time at which the object will hit the ground is 3 seconds.
Conclusion:
By calculating the time based on the vertical motion of the projectile, we confirm that the object will hit the ground after 3 seconds.
Important Questions from Motion in Two and Three Dimensions
A running truck at 54 km/hr is bought to rest in 10s. The distance travelled by the truck in 10th second is:
A balloon is moving upward with uniform acceleration g/8 cm/sec2 After half minute a body is dropped from them. The time taken by the body to reach on the ground is
The distances travelled by a body falling freely from rest in the first, second and third second are in the ratio
What will be the acceleration of a bus whose speed increases from 60 m/s to 100 m/s in 5s?
A cage in a mine-shaft descends with 2 ft/s2 units of acceleration. After it has been in motion for 10 seconds a particle is dropped on it from the top of the shaft with 32 ft/s2. What time elapses before the particle hits the cage?
