Answer:
a. Angle= 28.82°
b. Approved. Although he might feel cold, he should be able to cross.
Explanation:
Velocity Vector
Velocity is a measure of how quickly something is moving in a specific direction. It is represented as a vector that has both magnitude and direction. If an object can only move in one direction, then speed can serve as the scalar equivalent of that velocity (only focusing on magnitude).
a.
The explorer aims to swim across a river to reach his campsite, as depicted in the image below. The river's velocity is vr and the explorer's swimming speed in still water is ve. If he were to swim straight towards the campsite, he would end up downstream due to the river's current. Therefore, he must swim at an angle that allows him to overcome the current while still moving towards his goal. This angle relative to the shore is what we need to determine. The explorer's speed can be broken down into its horizontal (vx) and vertical (vy) components. In order to counteract the river's flow:
We can calculate the vertical component of the explorer's swimming speed as
Thus
Finding the value of 
Then the angle is given by
b.
The component of the explorer's velocity that goes horizontally is
This represents the actual velocity directed towards the campsite
Considering that
To find t
Calculating the duration for the explorer to cross the river
As this time is under the hypothermia threshold (300 seconds), the conclusion is
Approved. Although he will feel cold, he should manage to cross successfully.
1) The projectile's motion follows
,
In order to determine the velocity, we must compute the derivative of h(t):
Next, we will compute the speed at t=2 s and t=4 s:
The negative value of the second speed suggests that the projectile has already attained its highest point and is now descending.
2) The maximum height of the projectile occurs when its speed equals zero:
Thus, we have
And solving yields
3) To determine the maximum height, we substitute the time at which the projectile reaches this peak into h(t), specifically t=2.30 s:
4) The time at which the projectile lands is when the height reaches zero; h(t)=0, which leads to
This results in a second-degree equation, producing two answers: the negative root can be disregarded as it lacks physical significance; the second root is
, which indicates the landing time of the projectile.
5) The moment the projectile impacts the ground corresponds to the velocity at time t=4.68 s:
, carrying a negative sign to denote a downward direction.
Let Cp represent the specific heat of the metal object.
To find this, we can set up a heat balance equation (heat lost by metal = heat gained by water):
- 19g * Cp * (22degC – 96degC) = 75g * 4.184J/g degC * (22degC - 18degC)
<span>Cp = 0.893 J/g degC</span>
Answer:
Stars generate energy by the process of nuclear fusion.
They are large entities composed of gaseous elements.
The main constituents of stars are hydrogen and helium.
Explanation:
Stars are colossal objects with extensive gravitational forces causing them to contract, which allows fusion to take place: the atomic nuclei in the star's core are drawn very close together due to gravity and elevated temperatures, leading to the fusion reaction. This fusion serves as the energy output for a star.
Conversely, it is true that stars predominantly consist of hydrogen and helium (two hydrogen nuclei can fuse to become helium), which implies that a star is essentially an enormous ball of gas without a solid surface suitable for standing on.
As for the presence of water on a star, it is simply impossible. The extreme temperatures found in stars are far too high for water to exist in any liquid state on their surfaces.
