Physics, 15.07.2020 14:01, Jerrikasmith28

Two projectiles are thrown from the same point with the velocity of49ms-1. First is projected making an angle with the horizontal and the second at an angle of (90- ). The

second is found to rise 22.5m higher than the first. Find the heights to which each will rise?

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answered: dorindaramirez0531

Height of the first projectile = 49.98 m

Height of the second projectile = 72.52 m

Explanation:

From the given information;

Two projectiles are thrown from the same point with the velocity of49m/s

First is projected making an angle θ with the horizontal

and the second at an angle of 90 - θ.

Thus; for the first height to the horizontal; we have;

$H_1 = \dfrac{v^2 sin^2 \theta}{2g}$ ----- (1)

the second height in the vertical direction is :

$H_2 = \dfrac{v^2 cos^2 \theta}{2g}$ -----(2)

However; the second is found to rise 22.5 m higher than the first; so , we have :

$\dfrac{v^2 cos^2 \theta}{2g}= 22.5 + \dfrac{v^2 sin^2 \theta}{2g}$

Let's recall that :

Cos²θ = 1 - Sin²θ

Replacing it into above equation; we have:

$\dfrac{v^2}{2g} - \dfrac{v^2 sin^2 \theta}{2g}= 22.5 + \dfrac{v^2 sin^2 \theta}{2g}$

$\dfrac{v^2}{2g} - 22.5 = \dfrac{v^2 sin^2 \theta}{g}$

$\dfrac{1}{2 } \dfrac{v^2}{g} - 22.5 = \dfrac{v^2 sin^2 \theta}{g}$

$\dfrac{1}{2 } - \dfrac {9.8 \times 22.5}{(49)^2} = sin^2 \theta$

$\dfrac{1}{2 } - \dfrac {220.5}{2401} = sin^2 \theta$

$sin^2 \theta= 0.408$

From (1);

$H_1 = \dfrac{v^2 sin^2 \theta}{2g}$

$H_1 = \dfrac{49^2 \times 0.408}{2*9.8}$

$H_1 = \dfrac{979.608}{19.6}$

$\mathbf{H_1 =49.98 \ m }$

Height of the first projectile = 49.98 m

Similarly;

From(2)

$H_2 = \dfrac{v^2 cos^2 \theta}{2g}$

$H_2 = \dfrac{v^2 (1-sin^2 \theta)}{2g}$

$H_2 = \dfrac{49^2 (1-0.408 )}{2 \times 9.8}$

$H_2 = \dfrac{2401 (0.592 )}{19.6}$

$H_2 = \dfrac{1421.392}{19.6}$

$\mathbf{H_2 = 72.52 \ m}$

Height of the second projectile = 72.52 m

answered: Guest

c. 7/3

step-by-step explanation:

a rational number is like pi- it is a repeating decimal.

a. is -1.8

b. 2.236068

c. 2.3333333333333333333

d. is 3

i hope that ! =)

answered: Guest

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