Question

Your favorite professor decided to throw in the air a marker above his head (vertically). If the marker leaves his hand at a height of 1.2 m from the ground with an initial velocity of 20 m/s, when would the marker reach the highest point in the air (1.6 m from the ground)?

Answer 1

Note: The question has some ambiguity. The highest point cannot be the 1.6 m point. The highest point must be beyond that because if only g (acceleration due to gravity) is acting on the marker then it wont stop at 1.6 m, it'll fly beyond that point. I'm solving the question considering both things in separate parts.

PART A : Considering 1.6 m as a mid journey point, not the highest point. And solving for the time taken to reach 1.6 m.

Highest point reached by marker = 1.6 m

Point from which marker was thrown = 1.2 m

Hence, distance travelled by marker = 1.6 m - 1.2 m = 0.4 m

Displacement of marker = + 0.4 m (Assuming upward direction as positive.)

Initial velocity of marker = + 20 m/s (Assuming upward direction as positive)

Also, acceleration acting on marker = g = -9.8 m/s^2 (Assuming downward direction as negative)

Let, t be the time taken by marker to reach its highest position.

Applying motion equation:

Substituting values,

On solving the above quadratic equation:

t = 4.06 or 0.02 sec (There are two solutions, because after reaching the highest point the marker will come down again and cross the 1.6 m point.)

So, Time taken by marker to reach 1.6 m above ground = 0.02 sec

PART B : Considering highest point is somewhere above 1.6 m and solving for time taken to reach the highest point. Here, we only consider g (acceleration due to gravity) as the factor retarding the motion of the marker since we do not have any information about other retarding forces.

Initial velocity of marker = + 20 m/s (Assuming upward direction as positive)

Final velocity of marker = 0 m/s (Because marker will come to a halt at the highest point of its trajectory)

Also, acceleration acting on marker = g = -9.8 m/s^2 (Assuming downward direction as negative)

Let t be the time taken by the marker to reach its highest position.

Writing motion equation:

On solving, Time taken by marker to reach the highest point : t = 2.04 sec

PLEASE RATE IF YOU LIKE IT.