Answer:
a) , , b) , c) , d) , e)
Explanation:
a) The velocity function is determined by deriving the position function in time:
Velocities after 2 seconds and 4 seconds are, respectively:
b) The maximum height is reached when velocity is equal to zero:
The time when the projectile reaches the maximum height:
c) The maximum height is:
d) The projectile hits the ground when height is equal to zero:
The roots of the second order polynomial are presented below:
The first one is the only reasonable solution in physical terms.
e) The velocity of the projectile when it hits the ground is:
Answer:
When two forces acting on an object are equal in size but act in opposite directions, we say that they are balanced forces.
Explanation:
Answer:
A.Gravity acts to pull the object down
D.The object’s inertia carries it forward.
E.The path of the object is curved.
Explanation:
The motion of a projectile consists of two independent motions:
- A uniform motion along the horizontal direction, with constant horizontal speed
- A vertical motion with constant acceleration of g = 9.8 m/s^2 downward (acceleration due to gravity), due to the presence of the force of gravity, so the vertical velocity changes (increases in the downward direction)
As a result, the combined motion of the projectile has a curved trajectory (parabolic, more specifically). So the following options are correct:
A.Gravity acts to pull the object down --> gravity acts along the vertical direction
D.The object’s inertia carries it forward. --> there are no forces acting along the horizontal direction (if we neglect air resistance), so the horizontal motion continues with constant speed
E.The path of the object is curved
Answer:
Explanation:
The equation for this is the one for the Law of Momentum Conservation which says that the momentum before the collision of the balls has to be the same after the collision because momentum cannot be created or destroyed. For us in particular:
and filling in:
[(4.0)(6.0) + (2.0)(0)] = [(4.0 + 2.0)v] and
24 + 0 = 6.0v and
24 = 6.0v so
v = 4.0 m/s to the right
Chameleon tongue reaches 23 cm.
Train's final speed is 32 m/s.
The distance the tongue travels is divided into 2 phases.
1. The acceleration phase.
2. The coasting phase.
For the acceleration phase, the formula d = 0.5AT^2 determines how far the tongue travels while accelerating. The during the coasting phase, the tongue continues onward without changing its velocity, so it's formula is d = VT. The peak velocity of the tongue will be reached after 20 ms. So let's calculate it.
d = 0.5AT^2
d = 0.5*290 m/s^2 * (0.020 s)^2
d = 145 m/s^2 * 0.0004 s^2
d = 0.058 m
Now to handle coasting
d = 0.058 m + 0.030 s * 290 m/s^2 * 0.20 s
d = 0.058 m + 0.174 m
d = 0.232 m
Rounding to 2 significant digits gives 0.23 meters, or 23 cm.
For the train, we need to determine the acceleration. We know the velocity changed from 5.0 m/s to 14.0 m/s over a period of 8.0 seconds. So the acceleration is:
(14.0 m/s - 5.0 m/s)/8.0 s = (9.0 m/s)/8.0 s = 1.125 m/s^2
At the edge of town, the train is traveling at 14 m/s and accelerates at 1.125 m/s^2 for 16 seconds, so:
14 m/s + 1.125 m/s^2 * 16 s = 14 m/s + 18 m/s = 32 m/s
So the final speed of the train is 32 m/s