Which of the following are true for an object in projectile motion?
1 answer:
The correct options are: B, C and D.
In fact:
- B is true, because the motion of the projectile can be decomposed in two independent motions on the x and y axis. On the x-axis, there is no acceleration; while on the y-axis, the projectile is accelerating towards the ground with
(acceleration of gravity)
- C is true, because the two motions on the horizontal and vertical direction are independent. In particular, the horizontal motion is a uniform motion (constant velocity), while the vertical motion is a uniformly accelerated motion (because of the gravitational acceleration g acting on the projectile)
- D is true, in fact (if we neglect air resistance) gravity is the only force acting on the projectile.
In fact:
- B is true, because the motion of the projectile can be decomposed in two independent motions on the x and y axis. On the x-axis, there is no acceleration; while on the y-axis, the projectile is accelerating towards the ground with
- C is true, because the two motions on the horizontal and vertical direction are independent. In particular, the horizontal motion is a uniform motion (constant velocity), while the vertical motion is a uniformly accelerated motion (because of the gravitational acceleration g acting on the projectile)
- D is true, in fact (if we neglect air resistance) gravity is the only force acting on the projectile.
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Answer:
Explanation:
This is a 2D problem (parabolic) so we have to think that way. We have to split up the problem into its 2 dimensions to solve it. Think "y-stuff" and "x-stuff".
In the y-stuff category:
v₀ = 0 (initial upwards velocity is 0 since we are told the penny is thrown horizontally)
Δx = -10.0 m (this displacement is negative because the penny lands 10.0 m below the point from which it was thrown)
a = -9.8 m/s/s
t = ? (we need to find the time in this dimension so we can use it in the x dimension to find the displacement, our unknown)
In the "x-stuff" category:
v₀ = 7.25 m/s (this is given)
Δx = ???
a = 0 (acceleration in this dimension is ALWAYS 0)
t = (we will solve for this in the y-dimension and plug it in here).
In the y dimension:
Δx = v₀t + and plugging in from the y-dimension info:
which simplifies to
so
which, to 2 significant digits is
t = 1.4 seconds
Now we will do the same in the x-dimension, using t = 1.4:
Δx = v₀t + and filling in the x-stuff:
Δx = Notice that the stuff after the + sign goes to 0 cuz of the multiplication of 0, so what we are left with is another form of the d = rt equation:
Δx = 7.25(1.4) + 0 so
Δx = 1.0 × 10¹ m (That's rounded correctly to 2 sig dig's: 10 m from the base of the building).