A ball is thrown vertically upwards with an initial velocity of 30m/s. Calculate the maximum height that it reaches. Also calculate the time required to reach themaximum height. (use g = 10m/s2).
Answers
Answer :
11.467 metres (with respect to the pseudo datum) and 91.467 metres (with respect to ground)
31.777 m/s at 40 metres from the ground
42.3625 m/s at the ground level
Procedure-
We will be using the equations of motion in this case. And most importantly,
V^2 - U^2 = 2gS
Where
V= Final Velocity
U= Initial Velocity
g= acceleration due to gravity (9.81 m/s^2)
S= Distance covered.
For the first answer, we are supposed to find the maximum height. In that case, at the maximum height, the final velocity becomes 0 and the initial velocity (given) is 15 m/s. Put in the values in the above formula and get the value of S. HOLD ON! This is the distance from the pseudo datum (that is 80 metres from above the ground) and is not the actual maximum height. To find out the actual maximum height, add up 80 to the answer.
For this, we need to find out the speed at 40 metres above the ground. That also means that the ball has already travelled a distance of < the first answer> (minus) 40. This gives us the value of S. We know that at the top, the initial velocity will be 0 m/s. Put all the values in the given formula and get the value of V (final velocity).
For this, we require the final velocity at the ground level. That's simple. Put the value of S as that you get in the end of the first answer (total distance), U= 0 m/s and proceed in the given formula to find the value of V (at ground level).