Question

FORUM DESCRIPTION scussion Forum 2 Discussion Forum 2, post your response to the following discussion questions. Reply to at least two classmates' responses by the date indicated in Course Calendar. 1. Consider a two-dimensional projectile motion problem involving a ball starting and ending at the same height. The projectile leaves the ground with an initial velocity of 10 m/s at some angle theta with the horizontal, (a) What value of the angle theta (in degrees) makes the range of the projectile maximumExplain, (b) What is the range at this angle? (c) How long does it take for the ball to reach maximum height? (d) What is the maximum height? 2. A man is riding in a car that is moving at a constant speed along a horizontal, straight-line path. The rider throws a ball straight up to a height a few meters above his head. Ignoring air resistance, where will the ball land? 3. A child is driving a bumper car at an amusement park. During one interval of the ride, she is traveling at the car's maximum speed when she crashes into a bumper attached to one of the side walls. During the collision, her glasses fly forward from her face. Use Newton's laws of motion to explain why the glasses flew from her face? 4. An astronaut is on a spacewalk outside a spaceship in "gravity-free" space. Initially, the spaceship and astronaut are at rest with respect to each other. Then, the astronaut pushes to the left on the spacecraft. What will happen to the astronaut as a result of the push? To what direction will the astronaut accelerate? Why? MacBook Air

Answer 1

Solution :-

Solution to question 1 is based on the concept of projectile motion, where we study motion a particle given some initial velocity at an angle $\theta$ with respect to horizontal, in two dimensions separtely.and question 2 is simple and just require some knowledge of relative motion, as the relative velocity of ball with respect to person in the car is zero (because they have same velocity along +ve x-axis) so they move together as they were earlier along x-axis.

while question 3 & 4 is based on the concept of Newtons laws of motion.

Please read solution carefully and feel free to ask any doubt you face while understanding my solution. I would be happy to help.

vo Solho The initial velocity (86) of projectle %= lomls at an angle Q with horizontal Range (R) of projectile - R=vhsin 20 10 R 2-) g 1 in equation us and graceleration due to gravity) constant to to maximize the Range R) 0 can be varied as 2 R = 0 Sin2o - R will be maximum when Su 20=1 هه Sin 20= 1 20-t - Q = I or 45° Rmaximum = 82 sim 2 x 45 maximum (g. 1om/s) g loxlox max - lom 16 (C) & Po calculate time required to reach manimum height Let's use first equation of motion for vertical direction along y-ancis * Maximum height is achieved while going upwards, when the vertical component of velocity becomes zero.. initial velocity into two components: y coso ( + 4 sino a ya so recolving

and let Vy be vertical velocity at any time t, due to presence of (gl acceleration due to gravity downw. ards, vertical velocity decreases continuously finally becomes Zero (Vy=0) at maximum height, e-utat y = Boy - gt for manimum height from ea. 0 , we have 0 = 8 sino - gt So We have 4 y=0 t= usio g (d) from Second equation of motion for vertical motion ? h = q sind. t - 3 g + 2 for h to be maximum height (Himan 9 t = vosmo calculated in(e) part equation ③ becomes : - Vosino. Uosino sin²o g Н. man d x 4² sino مه 92 H man ² sinho 99

2 १ 2) The ball will land in the hands of a man, who throws the ball, because, het constant velocity of Car to be ų taward the n-auis. when the person throws the ball the have velocity & cas same that of car) towards the x-anis, as air resistance is Zero the ball always has this velocity uc towards tve x-areis, for vertical motion, acceleration due to gravity (g) is present downwards. So whatever is initial vertical velocity given to the ball by person continues to decrease then some time later becomes Kero on reaching maximum height, (but it has e towars - ames) and reverses the direction of motion. In car has travelled with ve towards the x-anis, het in ball reaches the car, so the car will also takes to reach the place where ball lands, because ball as well as both has velocity (U) towards the n-areis 3.) This situation is based concept of Newton's First law of motion or law of inertia, when Collision happened, just before this incident the car along moving forward and because collision motion stops to the glasses continued moving forward because there was them on her face during collision. tve the mean while time t time t car same on the with child was too little force acting on to hold

9 4.) According to Newton's third law of motion, if Astronant pushes on the spacecraft, it will push back on him with equal and opposite force. As action and reaction are equal and opposite. Both will be accelerated & as there is net each of them and they will drift aparat. They move at different rates, since, they have different masses. force on
Both astronaut and spaceship will accelerate in opposite directions.