Question

An object is vertically projected with an initial velocity of 20 m/s. Find the distance travelled in meters by the object in three seconds.
A. 10
B. 15
C. 20
D. 25

Answer 1

Hint: When an object is projected, the only force acting on it is force due to gravity. The acceleration due to gravity is a constant and hence we can use the equation of motion to determine the distance travelled by the object in three seconds.

Formula used: Distance travelled by the object, $s=ut+\dfrac{1}{2}a{{t}^{2}}$
Where $s$ is the distance travelled, $u$ is the initial velocity of the object in the direction distance is being measured, $a$ is the acceleration in the corresponding direction and $t$ is the time period.

Complete step by step answer:
When an object is projected, the only force acting on it just after projection is the gravitational force of the earth. Although other forces like air resistance act upon it but their magnitude can be neglected in comparison with gravitational force. The distance travelled along one direction by the projected object at any instant of time can be given by the equation of motion.
$s=ut+\dfrac{1}{2}a{{t}^{2}}$
Where $s$ is the distance travelled, $u$ is the initial velocity of the object in the direction distance is being measured, $a$ is the acceleration in the corresponding direction and $t$ is the time period.
Since the object is projected vertically upward with initial velocity of $u=20\text{ }m/s$. The acceleration is the acceleration due to gravity ($g$) which is acting in downward direction, we can write distance travelled as
$s=20t-\dfrac{1}{2}g{{t}^{2}}$
Substituting the values in the equation, the distance travelled in meters by the object in three seconds is
$s=20\times 3-\dfrac{1}{2}\times 10\times {{3}^{2}}$
On solving, we get
$s=15m$
Therefore, the distance travelled in meters by the object in three seconds is $15$.

So, the correct answer is “Option B”.

Note: The motion of the object under the influence of gravity only after projection is known as projectile motion. The distance travelled by the object depends on the angle on which it is projected. It travels maximum horizontal distance if projected at forty-five degrees.