Lesson 3, Topic 5
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Worked Examples – Projectile

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Example:

An missile is fired at a speed of 200ms-1 at an angle of 45°.

Find;
(i) The height attained by the missile.
(ii) How long it stays in the air?
(iii) The horizontal range.

Solution:

θ = 45°, U = 200ms-1, g = 10ms-2

(i) Height attained = $$\frac {U^2 Sin^2θ}{2g}$$

H = $$\frac {200^2 \: \times \: (0.7071)^2 }{20}$$

H = $$\frac {200^2 \: \times \: 0.5 }{20} = \frac {2000}{20}$$

H = 1000m.

(ii) Time of Flight, T = $$\frac {2U Sinθ}{g}$$

= $$\frac {2\: \times\: 200\: \times \:sin45^{\circ}}{10}$$

= $$\frac {400 \: \times \: 0.6494 }{10} = \frac {259.779}{10}$$

= 25.97Secs

(iii) Range =$$\frac {U^2 Sin2θ}{g}$$

= $$\frac {200^2 \: \times \: Sin2 \: \times \: 45}{10}$$

= $$\frac {200^2 \: \times \: Sin90}{10}$$

= $$\frac {40000 \: \times \: 1}{10}$$

= 4000m

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