Answer:
The snowball's speed after the impact is 3 m/s
Explanation:
Given the following:
mass of each ball
m₁ = 0.4 Kg
m₂ = 0.6 Kg
initial speed of both balls = v₁ = 15 m/s
Speed of 1 Kg mass post-collision =?
Applying conservation of momentum
m₁ v₁ - m₂ v₁ = (m₁+m₂) V
A negative velocity indicates that the second ball moves in the opposite direction.
0.4 x 15 - 0.6 x 15 = (1) V
Therefore,
V = - 3 m/s
Consequently,
The snowball's speed following the collision is 3 m/s
Answer:
Explanation:
According to the principle of energy conservation
all kinetic energy will change into thermal energy to increase its temperature
Next, divide both sides by the object's mass
the resulting temperature change is expressed as
The ideal launch angle of 45° for achieving the greatest horizontal distance is only applicable when the starting height matches the final height.
<span>In this scenario, you can demonstrate it as follows: </span>
<span>the initial velocity is Vo </span>
<span>the launch angle is α </span>
<span>the initial vertical velocity is </span>
<span>Vv = Vo×sin(α) </span>
<span>horizontal velocity becomes </span>
<span>Vh = Vo×cos(α) </span>
<span>the total flight duration is the period required to return to a height of 0 m, thus </span>
<span>d = v×t + a×t²/2 </span>
<span>where </span>
<span>d = distance = 0 m </span>
<span>v = initial vertical velocity = Vv = Vo×sin(α) </span>
<span>t = time =? </span>
<span>a = gravitational acceleration = g (= -9.8 m/s²) </span>
<span>therefore </span>
<span>0 = Vo×sin(α)×t + g×t²/2 </span>
<span>0 = (Vo×sin(α) + g×t/2)×t </span>
<span>t = 0 (obviously, the projectile is at height 0 m at time = 0s) </span>
<span>or </span>
<span>Vo×sin(α) + g×t/2 = 0 </span>
<span>t = -2×Vo×sin(α)/g </span>
<span>Now let's examine the horizontal distance. </span>
<span>r = v × t </span>
<span>where </span>
<span>r = horizontal range =? </span>
<span>v = horizontal velocity = Vh = Vo×cos(α) </span>
<span>t = time = -2×Vo×sin(α)/g </span>
<span>therefore </span>
<span>r = (Vo×cos(α)) × (-2×Vo×sin(α)/g) </span>
<span>r = -(Vo)²×sin(2α)/g </span>
<span>To find the extreme points of r (max or min) with respect to α, the first derivative of r with regards to α must be determined and set to 0. </span>
<span>dr/dα = d[-(Vo)²×sin(2α)/g] / dα </span>
<span>dr/dα = -(Vo)²/g × d[sin(2α)] / dα </span>
<span>dr/dα = -(Vo)²/g × cos(2α) × d(2α) / dα </span>
<span>dr/dα = -2 × (Vo)² × cos(2α) / g </span>
<span>As Vo and g are constants that are not equal to 0, the only solution for dr/dα to equal 0 is when </span>
<span>cos(2α) = 0 </span>
<span>2α = 90° </span>
<span>α = 45° </span>
The intensity of the sound increases because sound waves are mechanical waves, meaning they cannot move through a vacuum and require a medium to propagate.
