Question

At t = 0 seconds, a ball is thrown straight upwards from the edge of 50m-high building,
with a velocity of 10 m/s. If there is no air resistance, the ball hits the ground after:



(b) In the expression E=1\2 C (L\T)^2 ,L is measured in meters, t is measured in seconds and
E is measured in (Newton . meter), what is the unit of the symbol C , and what does it
physically represent?
a) Newton.meter; it represents force
b) Kg; it represents mass
c) m/s; it represents speed
d) m/s; it represents velocity
e) None of the above

Answer 1

Answer on Question #40959, Physics, Mechanics

(a) At $t = 0$ seconds, a ball is thrown straight upwards from the edge of 50m-high building, with a velocity of $10 \, \text{m/s}$. If there is no air resistance, the ball hits the ground after:

(b) In the expression $E = 1 \cdot 2 C (L \cdot T)^2$, $L$ is measured in meters, $t$ is measured in seconds and $E$ is measured in (Newton meter), what is the unit of the symbol $C$, and what does it physically represent?

a) Newton meter; it represents force

b) Kg; it represents mass

c) m/s; it represents speed

d) m/s; it represents velocity

e) None of the above

Solution:

(a)

An object in free fall experiences an acceleration $g$ of $-9.81 \, \text{m/s}^2$. (The sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is $-9.8 \, \text{m/s}^2$ for any freely falling object.

The kinetic equation is

$$y = y_0 + v_0 t + \frac{1}{2} a t^2$$

where

$y_0 = 50 \, \text{m}$ is initial position

$v_0 = 10 \, \text{m/s}$ is initial speed

$a = g = -9.81 \, \text{m/s}^2$ is acceleration

At time $t = ?$, the position of a ball is $y = 0$

Thus,

$$- \frac{1}{2} \cdot 9.81 \cdot t^2 + 10 t + 50 = 0$$

The solutions of quadratic equation are:

$$t = -2.33217$$ $$t = 4.3709$$

We choose positive solution.

So, the ball hits the ground after $t = 4.37 \, \text{s}$.

(b)

$$E = \frac{1}{2} C \left(\frac{L}{T}\right)^2$$

From this

$$C = \frac {2 E T ^ {2}}{L ^ {2}} = \left[ \frac {N \cdot m \cdot s ^ {2}}{m ^ {2}} \right] = \left[ \frac {N \cdot s ^ {2}}{m} \right]$$

newton (N) = kg·m/s²

Thus,

$$C = \left[ \frac {k g \cdot m \cdot s ^ {2}}{m \cdot s ^ {2}} \right] = [ k g ]$$

Answer. (a) $t = 4.37 \, \text{s}$,

(b) b) Kg; it represents mass.