A projectile is launched at an angle of .
a. Is there any point on the trajectory where and are parallel to each other? If so, where?
b. Is there any point where and are perpendicular to each
other? It so, where?
a. and do not become parallel to each other at any point on the trajectory.
b. and become perpendicular to each other at the highest point on the trajectory.
The initial velocity of the object is . Since, it is given that the projectile is launched at an angle is in a direction that makes an angle with the -axis. Let's resolve in to and components; and .
The only force acting on the object is the weight. Hence the acceleration of the object is equal to the gravitational acceleration , which always acts downward (in negative -direction).
Consider the horizontal motion. Since there is no acceleration in the -direction, remains unchanged during the projectile.
Now consider the vertical motion. Due to the gravitational acceleration in the negative direction , reduces and becomes zero. Now since there is no vertical velocity the object can't go higher than this point; this is the maximum height of the projectile.
After that the vertical motion of the object is like a free fall.
Let's say the maximum height it reaches is and the final displacement is . The path of the projectile can be sketched as given below.
From the diagram above we can see that, and do not become parallel to each other at any point on the trajectory.
From the diagram above we can see that, and become perpendicular to each other at the highest point on the trajectory.
While driving north at during a rainstorm you notice that the rain makes an angle of with the vertical. While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. From these observations, determine the speed and angle of the raindrops relative to the ground.
6. A rocket-powered hockey puck moves on a horizontal frictionless table. FIGURE EX4.6 shows graphs of and , the x - and y-components of the puck's velocity. The puck starts at the origin.
a. In which direction is the puck moving at ? Give your answer as an angle from the x-axis.
b. How far from the origin is the puck at ?
Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes to speed up from rest to its top speed of rotation every . The astronaut is strapped into a seat from the axis.
a. What is the astronaut’s tangential acceleration during the first ?
b. How many g’s of acceleration does the astronaut experience when the device is rotating at top speed? Each of acceleration is .
94% of StudySmarter users get better grades.Sign up for free