A ball is thrown upward at a 45^∘ angle. In the absence of air resistance, the ball follows a a.

A ball is thrown upward at a 45^∘ angle. In the absence of...

Key Concepts

Parabolic Trajectory

A parabolic trajectory is the specific curved path followed by a projectile under the influence of gravity. Because the horizontal motion is constant and the vertical motion is uniformly accelerated, the overall path of the projectile is a parabola, which is a quadratic curve.

Projectile Motion

Projectile motion refers to the motion of an object that is thrown or projected into the air and is influenced only by gravity (assuming air resistance is negligible). This type of motion is characterized by the constant horizontal velocity combined with a vertically accelerated motion due to gravity, which together produce a curved trajectory.

Transcript

00:02 Hi, here in this given problem, based upon this paragraph there are three different questions.

00:08 First of all, the paragraph says the two curves are here.

00:18 One of them is for the vertical motion of a projectile and another one is for the horizontal component of this motion.

00:32 Vertical component and horizontal component this is v y which is measured in meter per second and this is time t and here this is v x this is also measured in meter per second and this is time t now the curve for this velocity that is a straight line the maximum velocity when the time was zero and then it is start decreasing as the project projectile goes up then at the maximum height the velocity the vertical component of the velocity must have become zero then the projectile start coming back and here this time is given as t1 and this is the time given as twice of t1 the value of the velocity here this is given as 10 means 10 meter per second and here this is missing k which we will have to find and for the horizontal component means component of the velocity along horizontal this is simply remains constant throughout the motion of the projectile in the air and that is like this and its value is given as that is also 10 meter per second so it it means horizontal component of initial velocity that is equal to vertical component of initial velocity which is given as 10 meter per second.

02:19 So the net velocity will be given by and this here we are doing question number 156 based upon this paragraph.

02:31 So this vo will be given by square root of square of vox.

02:36 Plus square of v -o -y means this is 10 square plus 10 square or it comes out to be equal to 10 root 2 meter per second now in time t1 vy y vertical component of the velocity has become 0 so t1 is the time to go up to the maximum height.

03:38 So using first equation of motion, vf is equal to v i plus g t, vf, vertical component at the maximum height that is 0, and this is 10 initial vertical velocity, acceleration due to gravity that is g minus g into time t 1.

04:00 So this t1 here comes out to be equal to 10 by g, which is the answer for this problem number 156...

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