Answer:

Explanation:
<u>2-D Projectile Motion</u>
In 2-D motion, there are two separate components of the acceleration, velocity and displacement. The horizontal component has zero acceleration, while the acceleration in the vertical direction is always the acceleration due to gravity. The basic formulas for this type of movement are






The projectile is fired in such a way that its horizontal range is equal to three times its maximum height. We need to find the angle \theta at which the object should be launched. The range is the maximum horizontal distance reached by the projectile, so we establish the base condition:


Using the formulas for 

Simplifying

Dividing by 

Rearranging



The period of the block's mass is changed by a factor of √2 when the mass of the block was doubled.
The time period T of the block with mass M attached to a spring of spring constant K is given by,
T = 2π(√M/K).
Let us say that, when we increased the mass to 2M, the time periods of the block became T', the spring constant is not changed, so, we can write,
T' = 2π(√2M/K)
Putting T = 2π(√M/K) above,
T' =√2T
So, here we can see, if the mass is doubled from it's initial value. The time period of the mass will be changed by a factor of √2.
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The inflated balloon shrinks when it is placed in an ice bath with no change in atmospheric pressure.
<u>Explanation:</u>
When the inflated balloon is subjected to an ice bath, it shrinks. This is due to the fact that smaller volume gets occupied by the air/gas inside the balloon as the temperature decreases. Hence, causes the balloon walls to collapse.
An ice bath also lowers the overall air temperature of the balloon inside. As the temperature decreases, the air molecules move more slowly and with lower energy. Because of the particle's lower energy, their collisions with the walls are not enough to keep the inflated balloon.