Question:

Suppose an object is thrown with an initial speed of 10 ms^-1 at an angle 45⁰ with the horizontal,what is the range covered? Suppose the same object is thrown similarly in the moon, will there be any change in the range?If yes, what is the change? (Acceleration due to gravity in the moon g_moon =1/6g)

Solution:

Projectile motion and factors that affect the flight of a projectile:

education.pxf.io/75YQ33

Range of the projectile: (Projected in the Earth’s surface)

Range of a projectile is given by $${R=\frac{u^2\sin2\theta}{g}}$$

Initial speed of the projectile u = 10 ms^-1

Acceleration due to gravity g = 9.8 ms^-2

Angle of projection =45^o

$${R_E=\frac{10^2 \ sin 2(45)}{9.8}}$$

$${R_E=\frac{100\ \ sin90}{9.8}}$$

$${R_=\frac{100(1)}{9.8}}$$

$${R_E=10.2 \ m}$$

Range of the projectile on the Earth’s surface = 10.2 m

Range of the projectile (Thrown in the moon)

Since the gravity on the Moon is smaller than the gravity on the Earth, the range of the projectile will increase.

$${R_M=\frac{100 \ \sin 90}{\frac{g}{6}}}$$

$${R_M=6(\frac{100 \ \sin90}{9.8})}$$

$${R_M =6 \ R_E}$$

$${R_M = 6(10.2)}$$

$${R_M=61.2 m}$$

Range of the projectile in the moons surface =61.2 m

Range attained on the moon is approximately 6 times the range that on Earth.

Projectile motion:

Range of a projectile:

TRIGONOMETRIC VALUES:

Why the range of the projectile changes on the moon?

The range of a projectile on the moon is approximately 6 times greater than its range on Earth when projected with same initial velocity and same projection angle with the horizontal. This increase in range is due to the Moon’s significantly lower gravitational acceleration compared to the Earth.

Conclusion:

Initial speed of the projectile (in both cases) = 10 ms^-1

Angle of projection (in both cases) = 45^o

Range of the projectile on the Earth’s surface = 10.2 m

Range of the projectile in the moons surface =61.2 m

Range attained on the moon is approximately 6 times the range that on Earth.

The increase in range is due to the Moon’s significantly lower gravitational acceleration compared to the Earth.