Name: Speed and Velocity in Daily Life
Uploaded: 2019-07-19
Duration: 2 min 18 s
Description: Our life would be nothing without motion! So, let's dig a little deeper and see what motion entails. Watch this video to learn all about speed and velocity.

Question

A stone is catapulted at time

t = 0

, with an initial velocity of magnitude

18.0 m s^{- 1}

at

40.0 °

above the horizontal. What are the magnitudes of the (a) horizontal and
(b) vertical components of its displacement from the catapult site at

t = 1.10 s

? Repeat for the (c) horizontal and (d) vertical components at

t = 1.80 s

and for the (e) horizontal and (f) vertical components at

t = 5.00 s

Accepted Answer

The horizontal component of velocity, $u_{x} = 18 \cos (40 °)$ .
The vertical component of velocity, $u_{y} = 18 \sin (40 °)$ .

(a) At, $t = 1.10 s$ , the horizontal displacement $d_{x}$ is given by,
$d_{x} = u_{x} t = 18 \cos (40 °) \times 1.10 = 15.17 m$ .

(b) The vertical displacement will be(the acceleration along vertical direction is $- g = - 9.8 {ms}^{- 2}$ )
$d_{y} = u_{y} t - \frac{1}{2} g t^{2} = 18 \sin (40 °) \times 1.10 - 0.5 \times 9.8 \times {(1.10)}^{2} = 6.8 m$ .

(c) At, $t = 1.80 s$ , the horizontal displacement $d_{x}$ is given by,
$d_{x} = u_{x} t = 18 \cos (40 °) \times 1.80 = 24.82 m$ .

(d) The vertical displacement will be,
$d_{y} = u_{y} t - \frac{1}{2} g t^{2} = 18 \sin (40 °) \times 1.80 - 0.5 \times 9.8 \times {(1.80)}^{2} = 4.95 m$ .

(e) At, $t = 5.00 s$ , the horizontal displacement $d_{x}$ is given by,
$d_{x} = u_{x} t = 18 \cos (40 °) \times 5.00 = 68.94 m$ .
Note: This is greater than the range of the projectile, $R$ which is only possible if the projectile is thrown from a certain height. Else,
$d_{x} = R = \frac{u^{2} \sin (2 θ)}{g} = \frac{{(18.0)}^{2} \sin (2 \times 40 °)}{9.8} = 32.56 m$ .

(f) The vertical displacement will be,
$d_{y} = u_{y} t - \frac{1}{2} g t^{2} = 18 \sin (40 °) \times 5.00 - 0.5 \times 9.8 \times {(5.00)}^{2} = - 64.65 m$ .
Note: This is below the horizontal plane, which is possible only if the projectile is thrown from a certain height. Else,
$d_{y} = 0 m$ .

Important Questions on Motion in Two and Three Dimensions

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