The object will strike the ground at a distance of [tex]\boxed{15\text{ m}}[/tex] from the base of the cliff.
Further explanation:
This is a problem of projectile motion. When an object is thrown horizontally from a certain height, the object moves both in X and Y direction under the action of the acceleration due to gravity.
Given:
The initial velocity with which an object is thrown horizontally is [tex]5.0\text{ m/s}[/tex].
The object strikes the ground [tex]3.0\text{ s}[/tex] later so the total time of flight is [tex]3.0\text{ s}[/tex].
Concept:
First we choose the coordinate axis.
So let’s assume east direction as the positive X axis and vertical upward direction as the positive Y axis.
During the whole flight object is subjected to a downward acceleration [tex]g[/tex]. In horizontal direction external force on the object is zero so acceleration in X direction will be zero.
Analyze the motion of object in both X and Y direction:
In X direction,
[tex]{a_x}=0\\{u_x}=5.0\,{\text{m/s}}[/tex]
Let the distance traveled by an object in X-direction is [tex]{S_{\text{x}}}[/tex].
Acceleration is defined as the rate of change of velocity. Here, in X direction the acceleration is zero; therefore velocity of object will remain same in X direction throughout the motion.
Use the second equation of motion:
[tex]{S_{\text{x}}}={u_{\text{x}}}t+\dfrac{1}{2}{a_{\text{x}}}{t^2}[/tex]
Substitute [tex]5.0\,{\text{m/s}}[/tex] for [tex]{u_x}[/tex], [tex]3\text{ s}[/tex] for [tex]t[/tex] and [tex]0[/tex] for [tex]{a_x}[/tex] in the above expression.
[tex]\begin{aligned}{S_{\text{x}}}&=\left( {5.0\,{\text{m/s}}} \right)\left( {3\,{\text{s}}} \right)+\frac{1}{2}\left( 0 \right){t^2}\\&=15.0\,{\text{m}}\\\end{aligned}[/tex]
Thus, the object will strike the ground at a distance of [tex]\boxed{15\text{ m}}[/tex] from the base of the cliff.
Learn More:
1. A 30kg box being pulled across a carpeted floor https://brainly.com/question/7031524
2. During soccer practice, maya kicked a soccer ball at 37 degree https://brainly.com/question/11023695
3. Conservation of momentum during collision https://brainly.com/question/9484203
Answer Details:
Grade: High School
Subject: Physics
Chapter: Projectile motion
Keywords:
object, horizontally, thrown, cliff, height, initial velocity, strikes, ground, base, 5m/s, 3 sec, distance, acceleration due to gravity, X direction, Y-direction.
