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A projectile is launched from the point (x = 0, y = 0), with velocity (12.0î + 49.0 j) m/s, at t = 0. (a) Make a table listing the projectile's distance T from the ori- gin at the end of each second thereafter, for 0 < t s 10 s. Tabulating the x and y coordinates and the compo- nents of velocity v, and v, will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the veloc- ity. Suggestion: Argue that if v is not perpendicular to r, then r must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain your method for solving part (c).

A projectile is launched from the point (x = 0, y = 0), with velocity (12.0î + 49.0 j) m/s, at t = 0. (a) Make a table listing the projectile's distance T from the ori- gin at the end of each second thereafter, for 0 < t s 10 s. Tabulating the x and y coordinates and the compo- nents of velocity v, and v, will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the veloc- ity. Suggestion: Argue that if v is not perpendicular to r, then r must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain your method for solving part (c).

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A projectile is launched from the point (x = 0, y = 0), with velocity (12.0î + 49.0 j) m/s, at t = 0. (a) Make a table listing the projectile's distance T from the ori- gin at the end of each second thereafter, for 0 < t s 10 s. Tabulating the x and y coordinates and the compo- nents of velocity v, and v, will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the veloc- ity. Suggestion: Argue that if v is not perpendicular to r, then r must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain your method for solving part (c).
Transcribed Image Text:A projectile is launched from the point (x = 0, y = 0), with velocity (12.0î + 49.0 j) m/s, at t = 0. (a) Make a table listing the projectile's distance T from the ori- gin at the end of each second thereafter, for 0 < t s 10 s. Tabulating the x and y coordinates and the compo- nents of velocity v, and v, will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the veloc- ity. Suggestion: Argue that if v is not perpendicular to r, then r must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain your method for solving part (c).
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