A body is thrown vertically upward with a velocity of 72 km/hr. Find the maximum height reached and the time taken to reach the height.
1 Answer
Solution:
Given,
Initial velocity (u) = 72 km/hr,
= \(\frac{72\times1000}{60\times60}\) m/s
= \(\frac{720}{36}\) m/s
= 20 m/s
Final velocity (v) = 0 m/s [ because the body is thrown vertically upward ]
Acceleration (a) = - g = -10 m/s2
Height reached (h) = ?
TIme taken (t) = ?
we have from the third equation of motion in straight line..
\(v^2=u^2+2as\)
Or, \(0^2=20^2+2\times(-10)\times h\) [ we consider s = h for object falling vertically upward or downward ]
Or, 0 = 400- 20h
Or, 20h = 400
Or, h = 400/ 20
∴ h = 20 m
Also, from the first equation of motion in a straight line, we have
v = u + at
Or, 0 = 20 + (-10)t
Or, -20 = -10t
∴ t = 2 s
Hence, the body reaches the height of 20 m in 2 seconds.
- If a body changes its position with respect to the surrounding objects, then the body is said to be in motion.
- If a body does not change its position with respect to the surrounding objects, then the body is said to be at rest.
- The fixed point, about which we describe the motion of a body is called the reference point.
- The physical quantity having only magnitude but not a fixed direction is called a scalar quantity.
- The physical quantity having both magnitude and direction is called a vector quantity.
- Distance is the total length between two points. Its SI unit is m.
- Displacement is the shortest between the initial and final points. Its SI unit is also a meter.
- The rate of the change of distance is called speed and the rate of change of the displacement is called the velocity.
- Speed is a scalar quantity but velocity and acceleration is a vector quantity.
- If a body covers an equal distance in an equal interval of time, then the motion of the body is called uniform motion.
- If a body doesn't cover an equal distance in an equal interval of time, then the motion of the body is called a variable or non-uniform motion.
- The motion of a body relative to another object or the reference frame is called relative motion.