The x axis of a trajectory represents its ____________.
Height in the vertical direction.
Displacement in the horizontal direction(my guess)
Longitude
Latitude
A person throws a rock horizontally off a cliff ata a speed of 9 m/s from a point 64.8 m above the ground. How long is the rock in the air?
13.2 s
26.4 s
3.64 s
5.14 s
A package falls from an airplane in level flight at constant speed. If air resistance can be neglected, how does the motion of the package look to the pilot.
The package appears to travel in the shape of a parabola.
The package appears to fall straight downward.
The package appears to travel backward.
The package appears to fall backward and downward.
A paintball is shot horizontally in the positive x direction. At time Trianglet after the ball is shot, it is 4 cm to the right and 4cm below it’s starting point. At time 2trianglet, what is the position of the ball relative to it’s starting point. Ignore air resistance.
12 cm to the right and 16 cm below
8cm to the right and 8 cm below
12 cm to the right and 8 cm below
8 cm to the right and 16 cm below
Please help me solve and give correct answers!
1st guess is good ... others?
I don’t have any more guesses... these are very hard and I can’t even get an answer close enough to any answer choices :(
But i guess for 2 I choose C., 3 I choose d and 4 B
2nd ... horizontal velocity is not a factor
... how long to fall from 64.8 m? ... gravitational acceleration
3rd ... package maintains same horizontal speed as plane
4th ... horizontal velocity is constant , vertical is accelerated by gravity
... horizontal displacement is vs. t , vertical displacement is vs. t^2
Can you just give me the answers? This is confusing and I still have no idea.
2nd ... h = 1/2 g t^2 ... 64.8 = 4.9 * t^2
3rd ... package stays in same horizontal position relative to plane
... pilot sees it drop straight down
4th ... the time is doubled
... so horizontal is doubled , and vertical is quadrupled (doubled squared)
To solve these questions, we need to understand the concepts of projectile motion and the relationship between time, distance, and velocity.
1) The x-axis of a trajectory represents its displacement in the horizontal direction. Therefore, the correct answer is "Displacement in the horizontal direction."
2) In this case, the rock is thrown horizontally, which means its initial vertical velocity is zero. The only force acting on it is gravity, which causes it to accelerate downward. We can use the equation for the vertical displacement of an object under constant acceleration:
y = y0 + v0y * t + (1/2) * a * t^2
where:
y is the vertical displacement from the initial point (ground level in this case),
y0 is the initial vertical position (64.8 m in this case),
v0y is the vertical component of initial velocity (0 m/s in this case, as the rock is thrown horizontally),
t is the time in seconds,
a is the acceleration due to gravity (-9.8 m/s^2 as it acts downward).
We need to solve for t when y = 0 (when the rock hits the ground). Rearranging the equation and substituting the values:
0 = 64.8 + 0*t - (1/2) * 9.8 * t^2
0 = 64.8 - 4.9 * t^2
Solving this quadratic equation will give us the time when the rock hits the ground. The correct answer is 3.64 s.
3) Since air resistance is neglected, the only force acting on the package is gravity. In the absence of air resistance, the motion of a falling object follows a vertical parabolic trajectory. Therefore, the correct answer is "The package appears to travel in the shape of a parabola."
4) Since the paintball is shot horizontally in the positive x-direction, its initial vertical velocity is zero. The only force acting on it is gravity, which causes it to accelerate downward.
At time t, the horizontal displacement is given as 4 cm to the right, and the vertical displacement is 4 cm below the starting point. This means the vertical velocity component increases by 4 cm/s every second.
After 2t, the horizontal displacement will still be 4 cm to the right, but the vertical displacement will be doubled since the velocity component keeps increasing by 4 cm/s every second. Therefore, the vertical displacement will be 8 cm below the starting point.
The correct answer is "8 cm to the right and 8 cm below."
So, the correct answers are:
1) Displacement in the horizontal direction.
2) 3.64 s
3) The package appears to travel in the shape of a parabola.
4) 8 cm to the right and 8 cm below.