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Projectile Motion Problem & Solution

Problem

A student sits atop a platform a distance h above the ground. He throws a large object horizontally with a speed u. A wind blowing parallel to the ground gives the object a constant horizontal acceleration with magnitude a. This results in the object reaching the ground directly under the student. Determine the height h in terms of u, a and g. Ignore the effect of air resistance on the vertical motion.

Solution

For vertical motion,

............*

For horizontal motion,

or ..............#

Putting from * in #,

or .

Sum of the coefficients in the expansion of $(x+y)^n$ ....

If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$